12.21. Unsolveable Problems (optional) (WORK IN PROGRESS)¶
12.21.1. Unsolveable Problems¶
<IP_ADDRESS>. Introduction¶
Even the best programmer sometimes writes a program that goes into an infinite loop. Of course, when you run a program that has not stopped, you do not know for sure if it is just a slow program or a program in an infinite loop. After “enough time”, you shut it down. Wouldn’t it be great if your compiler could look at your program and tell you before you run it that it will get into an infinite loop? To be more specific, given a program and a particular input, it would be useful to know if executing the program on that input will result in an infinite loop without actually running the program.
Unfortunately, the Halting Problem, as this is called, cannot be solved. There will never be a computer program that can positively determine, for an arbitrary program \(P\), if \(P\) will halt for all input. Nor will there even be a computer program that can positively determine if arbitrary program \(P\) will halt for a specified input \(I\). How can this be? Programmers look at programs regularly to determine if they will halt. Surely this can be automated. As a warning to those who believe any program can be analyzed in this way, carefully examine the following code fragment before reading on.
while n > 1:
if ODD(n):
n = 3 * n + 1
else:
n = n / 2
This is a famous piece of code. The sequence of values that is assigned to \(n\) by this code is sometimes called the Collatz sequence for input value \(n\). Does this code fragment halt for all values of \(n\)? Nobody knows the answer. Every input that has been tried halts. But does it always halt? Note that for this code fragment, because we do not know if it halts, we also do not know an upper bound for its running time. As for the lower bound, we can easily show \(\Omega(\log n)\).
Todo
- type: Exercise
Need an exercise to study lower bound on Colletz function
Personally, I have faith that someday some smart person will completely analyze the Collatz function, proving once and for all that the code fragment halts for all values of \(n\). Doing so may well give us techniques that advance our ability to do algorithm analysis in general. Unfortunately, proofs from computability—the branch of computer science that studies what is impossible to do with a computer — compel us to believe that there will always be another bit of program code that we cannot analyze. This comes as a result of the fact that the Halting Problem is unsolvable.
<IP_ADDRESS>. Uncountability¶
Before proving that the Halting Problem is unsolvable, we first prove that not all functions can be implemented as a computer program. This must be so because the number of programs is much smaller than the number of possible functions.
A set is said to be countable (or countably infinite if it is a set with an infinite number of members) if every member of the set can be uniquely assigned to a positive integer. A set is said to be uncountable (or uncountably infinite) if it is not possible to assign every member of the set to its own positive integer.
To understand what is meant when we say “assigned to a positive integer”, imagine that there is an infinite row of bins, labeled 1, 2, 3, and so on. Take a set and start placing members of the set into bins, with at most one member per bin. If we can find a way to assign all of the set members to bins, then the set is countable. For example, consider the set of positive even integers 2, 4, and so on. We can assign an integer \(i\) to bin \(i/2\) (or, if we don’t mind skipping some bins, then we can assign even number \(i\) to bin \(i\)). Thus, the set of even integers is countable. This should be no surprise, because intuitively there are “fewer” positive even integers than there are positive integers, even though both are infinite sets. But there are not really any more positive integers than there are positive even integers, because we can uniquely assign every positive integer to some positive even integer by simply assigning positive integer \(i\) to positive even integer \(2i\).
On the other hand, the set of all integers is also countable, even though this set appears to be bigger than the set of positive integers. This is true because we can assign 0 to positive integer 1, 1 to positive integer 2, -1 to positive integer 3, 2 to positive integer 4, -2 to positive integer 5, and so on. In general, assign positive integer value \(i\) to positive integer value \(2i\), and assign negative integer value \(-i\) to positive integer value \(2i+1\). We will never run out of positive integers to assign, and we know exactly which positive integer every integer is assigned to. Because every integer gets an assignment, the set of integers is countably infinite.
Are the number of programs countable or uncountable? A program can be viewed as simply a string of characters (including special punctuation, spaces, and line breaks). Let us assume that the number of different characters that can appear in a program is \(P\). (Using the ASCII character set, \(P\) must be less than 128, but the actual number does not matter). If the number of strings is countable, then surely the number of programs is also countable. We can assign strings to the bins as follows. Assign the null string to the first bin. Now, take all strings of one character, and assign them to the next \(P\) bins in “alphabetic” or ASCII code order. Next, take all strings of two characters, and assign them to the next \(P^2\) bins, again in ASCII code order working from left to right. Strings of three characters are likewise assigned to bins, then strings of length four, and so on. In this way, a string of any given length can be assigned to some bin.
By this process, any string of finite length is assigned to some bin. So any program, which is merely a string of finite length, is assigned to some bin. Because all programs are assigned to some bin, the set of all programs is countable. Naturally most of the strings in the bins are not legal programs, but this is irrelevant. All that matters is that the strings that do, correspond to programs are also in the bins.
Now we consider the number of possible functions. To keep things simple, assume that all functions take a single positive integer as input and yield a single positive integer as output. We will call such functions integer functions. A function is simply a mapping from input values to output values. Of course, not all computer programs literally take integers as input and yield integers as output. However, everything that computers read and write is essentially a series of numbers, which may be interpreted as letters or something else. Any useful computer program’s input and output can be coded as integer values, so our simple model of computer input and output is sufficiently general to cover all possible computer programs.
We now wish to see if it is possible to assign all of the integer functions to the infinite set of bins. If so, then the number of functions is countable, and it might then be possible to assign every integer function to a program. If the set of integer functions cannot be assigned to bins, then there will be integer functions that must have no corresponding program.
Imagine each integer function as a table with two columns and an infinite number of rows. The first column lists the positive integers starting at 1. The second column lists the output of the function when given the value in the first column as input. Thus, the table explicitly describes the mapping from input to output for each function. Call this a function table.
Next we will try to assign function tables to bins. To do so we must order the functions, but it does not matter what order we choose. For example, Bin 1 could store the function that always returns 1 regardless of the input value. Bin 2 could store the function that returns its input. Bin 3 could store the function that doubles its input and adds 5. Bin 4 could store a function for which we can see no simple relationship between input and output. 1 These four functions as assigned to the first four bins are shown in Figure 12.22.1.
Can we assign every function to a bin? The answer is no, because there is always a way to create a new function that is not in any of the bins. Suppose that somebody presents a way of assigning functions to bins that they claim includes all of the functions. We can build a new function that has not been assigned to any bin, as follows. Take the output value for input 1 from the function in the first bin. Call this value \(F_1(1)\). Add 1 to it, and assign the result as the output of a new function for input value 1. Regardless of the remaining values assigned to our new function, it must be different from the first function in the table, because the two give different outputs for input 1. Now take the output value for 2 from the second function in the table (known as \(F_2(2)\)). Add 1 to this value and assign it as the output for 2 in our new function. Thus, our new function must be different from the function of Bin 2, because they will differ at least at the second value. Continue in this manner, assigning \(F_{new}(i) = F_i(i) + 1\) for all values \(i\). Thus, the new function must be different from any function \(F_i\) at least at position \(i\). This procedure for constructing a new function not already in the table is called diagonalization. Because the new function is different from every other function, it must not be in the table. This is true no matter how we try to assign functions to bins, and so the number of integer functions is uncountable. The significance of this is that not all functions can possibly be assigned to programs, so there must be functions with no corresponding program. Figure 12.22.2 illustrates this argument.
<IP_ADDRESS>. The Halting Problem Is Unsolvable¶
There might be intellectual appeal to knowing that there exists some function that cannot be computed by a computer program But does it really matter if no program can compute a “nonsense” function such as the one shown in Bin 4 of Figure 12.22.1? That alone doesn’t have to mean that there is a useful function that cannot be computed. After all, the universe should not be this perverse, should it? Perhaps the very fact that we can easily specify the function that we want to compute implies that there must be an algorithm to compute it.
Unfortunately, not so. Now we will prove that the Halting Problem cannot be computed by any computer program. The proof is by contradiction.
We begin by assuming that there is a function named halt
that
can solve the Halting Problem.
Obviously, it is not possible to write out something that does not
exist, but here is a plausible sketch of what a function to solve the
Halting Problem might look like if it did exist.
Function halt
takes two inputs: a string representing the
source code for a program or function, and another string
representing the input that we wish to determine if the input program
or function halts on.
Function halt
does some work to make a decision (which is
encapsulated into some fictitious function named PROGRAM_HALTS
).
Function halt
then returns TRUE if the input program or
function does halt on the given input, and FALSE otherwise.
bool halt(String prog, String input) {
if (PROGRAM_HALTS(prog, input))
return true;
else
return false;
}
We now will examine two simple functions that clearly can exist because the complete code for them is presented here.
// Return true if "prog" halts when given itself as input
bool selfhalt(String prog) {
if (halt(prog, prog))
return true;
else
return false;
}
// Return the reverse of what selfhalt returns on "prog"
void contrary(String prog) {
if (selfhalt(prog))
while (true); // Go into an infinite loop
}
What happens if we make a program whose sole purpose is to execute
the function contrary
and run that program with itself as
input?
One possibility is that the call to selfhalt
returns TRUE
;
that is, selfhalt
claims that contrary
will halt when run on
itself.
In that case, contrary
goes into an infinite loop
(and thus does not halt).
On the other hand, if selfhalt
returns FALSE, then
halt
is proclaiming that contrary
does not halt on itself,
and contrary
then returns, that is, it halts.
Thus, contrary
does the contrary of what
halt
says that it will do.
The action of contrary
is logically inconsistent with the
assumption that halt
solves the Halting Problem correctly.
There are no other assumptions we made that might cause this
inconsistency.
Thus, by contradiction, we have proved that halt
cannot
solve the Halting Problem correctly, and thus there is no program that
can solve the Halting Problem.
Now that we have proved that the Halting Problem is unsolvable, we can use reduction arguments to prove that other problems are also unsolvable. The strategy is to assume the existence of a computer program that solves the problem in question and use that program to solve another problem that is already known to be unsolvable.
Example 12.22.1
Consider the following variation on the Halting Problem. Given a computer program, will it halt when its input is the empty string? That is, will it halt when it is given no input? To prove that this problem is unsolvable, we will employ a standard technique for computability proofs: Use a computer program to modify another computer program.
Proof by contradiction:
Assume that there is a function Ehalt
that determines
whether a given program halts when given no input.
Recall that our proof for the Halting Problem involved functions
that took as parameters a string representing a program and another
string representing an input.
Consider another function combine
that takes a program
\(P\) and an input string \(I\) as parameters.
Function combine
modifies \(P\) to store \(I\)
as a static variable \(S\) and further modifies all calls
to input functions within \(P\) to instead get their input from
\(S\).
Call the resulting program \(P'\).
It should take no stretch of the imagination to believe that any
decent compiler could be modified to take computer programs and
input strings and produce a new computer program that has been
modified in this way.
Now, take \(P'\) and feed it to Ehalt
.
If Ehalt
says that \(P'\) will halt, then we know that
\(P\) would halt on input \(I\).
In other words, we now have a procedure for solving the original
Halting Problem.
The only assumption that we made was the existence of Ehalt
.
Thus, the problem of determining if a program will halt on no input
must be unsolvable.
Example 12.22.2
For arbitrary program \(P\), does there exist any input for which \(P\) halts?
Proof by contradiction:
This problem is also uncomputable.
Assume that we had a function Ahalt
that, when given program
\(P\) as input would determine if there is some input for which
\(P\) halts.
We could modify our compiler (or write a function as part of a
program) to take \(P\) and some input string \(w\), and
modify it so that \(w\) is hardcoded inside \(P\),
with \(P\) reading no input.
Call this modified program \(P'\).
Now, \(P'\) always behaves the same way regardless of its
input, because it ignores all input.
However, because \(w\) is now hardwired inside of \(P'\),
the behavior we get is that of \(P\) when given \(w\) as
input.
So, \(P'\) will halt on any arbitrary input if and only if
\(P\) would halt on input \(w\).
We now feed \(P'\) to function Ahalt
.
If Ahalt
could determine that \(P'\) halts on some
input, then that is the same as determining that \(P\) halts on
input \(w\).
But we know that that is impossible.
Therefore, Ahalt
cannot exist.
There are many things that we would like to have a computer do that are unsolvable. Many of these have to do with program behavior. For example, proving that an arbitrary program is “correct”, that is, proving that a program computes a particular function, is a proof regarding program behavior. As such, what can be accomplished is severely limited. Some other unsolvable problems include:
Does a program halt on every input?
Does a program compute a particular function?
Do two programs compute the same function?
Does a particular line in a program get executed?
This does not mean that a computer program cannot be written
that works on special cases, possibly even on most programs that we
would be interested in checking.
For example, some C compilers will check if the control expression
for a while
loop is a constant expression that evaluates to
FALSE
.
If it is, the compiler will issue a warning that the while
loop code will never be executed.
Programmers find this special case useful enough to make it worth
including in the compiler.
However, it is not possible to write a computer program that can
check for all input programs whether a specified line of code
will be executed when the program is given some specified input.
Another unsolvable problem is whether a program contains a computer virus. The property “contains a computer virus” is a matter of behavior. Thus, it is not possible to determine positively whether an arbitrary program contains a computer virus. Fortunately, there are many good heuristics for determining if a program is likely to contain a virus, and it is usually possible to determine if a program contains a particular virus, at least for the ones that are now known. Real virus checkers do a pretty good job, but, it will always be possible for malicious people to invent new viruses that no existing virus checker can recognize.
- 1
There is no requirement for a function to have any discernible relationship between input and output. A function is simply a mapping of inputs to outputs, with no constraint on how the mapping is determined.


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Filter Messages By SQL92 In RocketMQ
So far, RocketMQ only support message filtering feature by TAG
, but one message only can own one tag, this is too limited to meet complex business requirements.
So, we want to define and implement a reasonable filter language based on a subset of the SQL 92 expression syntax to support customized message filtering.
Why Subset Of SQL92
Let RocketMQ has the ability of message filtering is the purpose of this issue, and as we know, SQL92 is used widely and most persons are familiar with it.It’s resonable to select it as RocketMQ’s grammar.
As I know, ActiveMQ already impllement this functionality based on JavaCC, it’s simple and exntensible.So I just extract it and integrate into RocketMQ, only some grammars:
- Numeric comparison, like
>
,>=
,<
,<=
,BETWEEN
,=
; - Character comparison, like
=
,<>
,IN
; IS NULL
orIS NOT NULL
;- Logical
AND
, logicalOR
, logicalNOT
;
Constant type are:
- Numeric, like 123, 3.1415;
- Character, like ‘abc’, must be maked with single quotes;
NULL
, special constant;- Boolean,
TRUE
orFALSE
;
Design
- Structure
- Broker collects the expression of consumer through heartbeat request, and saved in
ConsumerFilterManager
. - When consumer pulls messages, broker will construct a
MessageFilter
(an interface) with compiled expression and subscription data to select matched messages inCommitLog
.
The main logic is simple.
- New Module, rocketmq-filter
The implementation of SQL92 language is placed in this module which have dependency on common module.
Broker compile or evaluate expression through the interface of FilterSpi
contained in FilterFactory
that manage all FilterSpi
and also support new one to register.
- How to manage consumer’s expression data
Different from tag filtering, expression of SQL92 should be compiled first to check whether is leagal and then use the complied expression to compute. This procedure is designed to take place at broker.
ConsumerManager
manage the suscriptions of push consumer, and ConsumerFilterManager
manage the expression info of push consumer who wish to filter message by special language, the info includes data version, expression, compiled expression, alive time and etc.
- How to filter message by expression
I redesign the interface getMessage
of MessageStore
by replace the last parameter SubscriptionData
to MessageFilter
that is also refactored. The purpose is to make module rocketmq-store
has no relation with protocol.
When get message, the implementation ExpressionMessageFilter
would check whether the message is matched by BitsArray
which will be refered later or evaluation, just as the mechanism of tag filtering.
- Optimization, pre-calculate the filtering result when build consume queue
It’s poor performance to do filter when pull message:
- off-heap to heap, once every consumer subscribed same topic pull message.
- decode message properties, once every consumer subscribed same topic pull message.
BloomFilter
and pre-calculation are adopted to optimize the situation:
- Every consumer has been asigned some bit position of
BloomFilter
when register to broker. - When broker build queue after message into
CommitLog
, the consumer’s filtering result would be calculated, and all resuls are assembled as aBitsArray
saved inConsumeQueueExt
. ConsumeQueueExt
is a store file linked toConsumeQueue
,ConsumeQueue
could find the data by thetagsCode
whitch is already replaced by the address(for compitable, the range is Long.MIN_VALUE to Integer.MIN_VALUE) generated byConsumeQueueExt
.ExpressionMessageFilter
could use theBitsArray
to check whether the message is matched. Because of BloomFilter’s collision, it also need to decode properties to do calculation for matched message(may could be reduced by check the collision, not include in this edition).
This optimization is suitable for:
- High subscription ratio.
- Large properties.
This optimization is off default, it need set some configs when broker starting to switch on:
- enableCalcFilterBitMap = true, means to caculate bitmap when build consume queue.
- expectConsumerNumUseFilter = XX(Integer, default is 32), means estimated consumer num subscribe same topic.
- maxErrorRateOfBloomFilter = XX(1~100, default is 20), means error rate of bloom filter.
- enableConsumeQueueExt = true, means construct consume queue extend file.
Interface
Only push consumer could filter message by SQL92 expression in this edition, the interface is:
public void subscribe(final String topic, final MessageSelector messageSelector)
Performance Comparison
Configuration of broker machine: 32 core, 128G memory, 1000Mb/s full duplex dual network
Producer send message with 1k body and 1k properties.
Five consumers consume message through push model, every consumer would get 1/5 messages of total.
Cpu and gc frequency is about 30% lower when do pre-calculate filtering result.
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Python API¶
Cosmology Module¶
-
class
PerturbedHalos.Cosmology.
Cosmology
(redshift, name='', verb=False, **params)[source]¶ Class to hold the basic cosmology and CLASS attributes. This can be initialized by a set of cosmological parameters or a pre-defined cosmology.
Loaded cosmological models:
- Planck18: Bestfit cosmology from Planck 2018, using the baseline TT,TE,EE+lowE+lensing likelihood.
- Quijote: Fiducial cosmology from the Quijote simulations of Francisco Villaescusa-Navarro et al.
- Abacus: Fiducial cosmology from the Abacus simulations of Lehman Garrison et al.
Parameters: - redshift (float) – Desired redshift \(z\)
- name (str) – Load cosmology from a list of predetermined cosmologies (see above).
- params (kwargs) – Any other CLASS parameters.
Keyword Arguments: verb (bool) – If true output useful messages througout run-time, default: False.
-
compute_linear_power
(kh_vector, kh_min=0.0)[source]¶ Compute the linear power spectrum from CLASS for a vector of input k.
If set, we remove any modes below some minimum k.
Parameters: - kh_vector (np.ndarray) – Vector of wavenumbers (in h/Mpc units) to compute linear power with.
- kh_min (float) – Value of k (in h/Mpc units) below which to set \(P(k) = 0\), default: 0.
Returns: Linear power spectrum in \((h^{-1}\mathrm{Mpc})^3\) units
Return type: np.ndarray
Mass Function Module¶
-
class
PerturbedHalos.MassFunction.
MassFunction
(cosmology, mass_function_name='Crocce', verb=False, **mass_params)[source]¶ Class to hold a mass function for halos and associated bias.
Implemented Mass Functions:
- Sheth-Tormen: Sheth & Tormen 1999 analytic mass function. This assumes virialized halos, and uses the critical density from Nakamura & Suto 1997.
- Tinker: Tinker et al. 2010, eq. 8. This assume a spherical overdensity, the value of which can be specified.
- Crocce: Crocce et al. 2009, eq. 22. Calibrated from Friends-of-Friends halos with linking length 0.2
- Bhattacharya: Bhattacharya et al. 2010, eq. 12. Calibrated from Friends-of-Friends halos with linking length 0.2
Implemented Bias Functions:
- Sheth-Tormen Sheth-Tormen 2001, eq. 8 Associated to the ‘Sheth-Tormen’ mass function.
- Tinker: Tinker et al. 2010, eq. 15. Associated to the ‘Tinker’ mass function.
- Crocce: Peak-background split derivation from the ‘Crocce’ mass function of eq. 22, Crocce et al. 2009.
- Bhattacharya: Bhattacharya et al. 2010, eq. 18. Associated to the ‘Bhattacharya’ mass function.
Parameters: - cosmology (Cosmology) – Class instance containing relevant cosmological information
- mass_function_name (str) – Mass function to use (see above), default: ‘Crocce’
- mass_param (kwargs) – Any additional parameters to pass to the class. These include: - tinker_overdensity: (Only for the Tinker mass function): spherical overdensity defining halos, default: 200
Keyword Arguments: verb (bool) – If true output useful messages througout run-time, default: False.
-
linear_halo_bias
(m_h)[source]¶ Compute the linear halo bias, from the peak background split.
Associated bias functions are available for each mass function, and more can be user-defined. See the class description for details of the loaded parametrizations.
Parameters: m_h (np.ndarray) – Array of masses in \(h^{-1}M_\mathrm{sun}\) units. Returns: Linear Eulerian halo bias (dimensionless) Return type: np.ndarray
-
mass_function
(m_h)[source]¶ Return the mass function, equal to the number density of halos per unit logarithmic mass interval. This assumes the existence of a universal mass function, with
\[dn/d\log_{10}M = f(\sigma(M))\frac{\bar{\rho}_M}{M} \frac{d\ln\sigma(M)}{d\log_{10}(M)}\]where \(f\) is the universal mass function, \(\bar{\rho}_M\) is the mean matter density at redshift zero and \(\sigma^2(M)\) is the overdensity variance on spheres with a radius given by the Lagrangian radius for mass \(M\).
For details of the available mass function parametrizations, see the class description.
Note
For efficiency, we return the mass function \(\frac{dn}{d\log_{10}(M)}\) rather than the standard form \(\frac{dn}{dM}\).
Parameters: m_h (np.ndarray) – Array of masses in \(h^{-1}M_\mathrm{sun}\) units. Returns: Mass function, \(dn/d\log_{10}(M)\) in \(\mathrm{Mpc}^{-3}\) units Return type: np.ndarray
-
second_order_bias
(m_h)[source]¶ Compute the second order Eulerian bias, defined as \(\frac{4}{21}b_1^L + \frac{1}{2}b_2^L\) where \(b_1^L\) and \(b_2^L\) are the Lagrangian bias parameters.
Associated bias functions are available for each mass function, and more can be user-defined. See the class description for details of the loaded parametrizations.
Parameters: - m_h: Mass in \(h^{-1}M_\mathrm{sun}\) units.
Halo Physics Module¶
-
class
PerturbedHalos.HaloPhysics.
HaloPhysics
(cosmology, mass_function, concentration_name='Duffy', profile_name='NFW', logM_min=6, logM_max=17, npoints=100000, verb=False, tinker_overdensity=200)[source]¶ Class to hold halo model quantities and relevant integrals.
Implemented Concentration Functions:
- Duffy: Duffy et al. (2008) for virial-density haloes (second section in Table 1)
Implemented Halo Profiles:
- NFW: Navarro, Frenk & White (1997) universal halo profile. We use the virial collapse overdensity from Bryan & Norman 1998 to construct this.
Parameters: - cosmology (Cosmology) – Instance of the Cosmology class containing relevant cosmology and functions.
- mass_function (MassFunction) – Instance of the MassFunction class, containing the mass function and bias
- concentration_name (str) – Concentration parametrization to use (see above), default: ‘Duffy’
- profile_name (str) – Halo profile parametrization to use (see above), default: ‘NFW’
- hyperparams (kwargs) – Any additional parameters to pass to the class (see below).
Keyword Arguments: - logM_min (float) – Minimum mass in \(\log_{10}(M/M_\mathrm{sun})\), default: 6
- logM_max (float) – Maximum mass in \(\log_{10}(M/M_\mathrm{sun})\), default: 17
- npoints (int) – Number of sampling points for \(\sigma(M)\) interpolation, default: 1e5
- tinker_overdensity (int) – (Only for the Tinker mass function): spherical overdensity defining halos, default: 200
- verb (bool) – If true output useful messages througout run-time, default: False.
-
halo_concentration
(m_h)[source]¶ Compute the halo concentration \(c = r_\mathrm{virial} / r_\mathrm{scale}\).
For details of the available concentration parametrizations, see the class description.
Parameters: m_h (np.ndarray) – Mass in \(h^{-1}M_\mathrm{sun}\) units. Returns: Array of concentration parameters. Return type: np.ndarray
-
halo_profile
(m_h, k_phys, norm_only=False)[source]¶ Compute the halo profile function in Fourier space; \(\rho(k|m) = \frac{m}{\bar{\rho}_M}u(k|m)\) where \(\bar{\rho}_M\) is the background matter density and \(u(k|m)\) is the halo profile.
We assume halos have a virial collapse overdensity here, based on the parametrization of Bryan & Norman 1998.
For details of the available profile parametrizations, see the class description.
Parameters: - m_h (np.ndarray) – Mass in \(h^{-1}M_\mathrm{sun}\) units.
- k_phys (np.ndarray) – Physical wavenumber in 1/Mpc units.
- norm_only (bool) – Boolean, if set, just return the normalization factor \(m/\bar{\rho}_M\), default: False
Returns: Halo profile \(\rho(k|m)\) or \(m/\bar{\rho}_M\), if the norm_only parameter is set.
Return type: np.ndarray
Mass Integrals Module¶
-
class
PerturbedHalos.MassIntegrals.
MassIntegrals
(cosmology, mass_function, halo_physics, kh_vector, min_logM=6.001, max_logM=16.999, N_mass=10000, verb=False)[source]¶ Class to compute and store the various mass integrals of the form
\[I_p^{q1,q2}(k_1,...k_p) = \int n(m)b^{(q1)}(m)b^{(q2)}\frac{m^p}{\rho_M^p}u(k_1|m)..u(k_p|m)dm\]which are needed to compute the power spectrum model. Here \(b^{(q)}\) is the q-th order bias (with \(b^{0}=1\)), \(u(k|m)\) is the normalized halo profile and \(n(m)\) is the mass function.
All integrals are performed via Simpson’s rule over a specified mass range, and are simply returned if they are already computed.
For the \(I_1^{1,0} = I_1^1\) integral, the integral must be corrected to ensure that we recover the bias consistency relation \(I_1^1 \rightarrow 1\) as \(k \rightarrow 0\).
This requires an infinite mass range, so we instead approximate;
\[I_1^1(k)_{\mathrm{corrected}} = I_1^1(k) + ( 1 - I_1^1(0) ) \frac{u(k|m_min)}{u(k|0)}\]for normalized halo profile \(u(k|m)\).
Parameters: - cosmology (Cosmology) – Instance of the Cosmology class containing relevant cosmology and functions.
- mass_function (MassFunction) – Instance of the MassFunction class, containing the mass function and bias.
- halo_physics (HaloPhysics) – Instance of the HaloPhysics class, containing the halo profiles and concentrations.
- kh_vector (np.ndarray) – Array (or float) of wavenumbers in \(h\mathrm{Mpc}^{-1}\) units from which to compute mass integrals.
Keyword Arguments: - min_logM (float) – Minimum mass in \(\log_{10}(M/M_\mathrm{sun})\) units, default: 6.001.
- max_logM (float) – Maximum mass in \(\log_{10}(M/M_\mathrm{sun})\) units, default: 16.999.
- N_mass (int) – Number of logarithmically spaced mass grid points, default: 10000.
- verb (bool) – If true output useful messages througout run-time, default: False.
-
compute_I_00
()[source]¶ Compute the I_0^0 integral, if not already computed.
Returns: Value of \(I_0^0\) Return type: float
-
compute_I_01
()[source]¶ Compute the I_0^1 integral, if not already computed.
Returns: Value of \(I_0^1\) Return type: float
-
compute_I_11
(apply_correction=True)[source]¶ Compute the \(I_1^1(k)\) integral, if not already computed. Also apply the correction noted in the class header if required.
When computing \({}_i J_1^1\) type integrals (over a finite mass bin), the correction should not be applied.
Keyword Arguments: apply_correction (bool) – Whether to apply the correction in the class header to ensure the bias consistency relation is upheld. Returns: Array of \(I_1^1\) values for each k. Return type: np.ndarray
-
compute_I_111
()[source]¶ Compute the \(I_1^{1,1}(k)\) integral, if not already computed.
Returns: Array of \(I_1^{1,1}\) values for each k. Return type: np.ndarray
-
compute_I_12
(apply_correction=True)[source]¶ Compute the \(I_1^2(k)\) integral, if not already computed. Also apply the correction noted in the class header if required.
When computing \({}_i J_1^2\) type integrals (over a finite mass bin), the correction should not be applied.
Keyword Arguments: apply_correction (bool) – Whether to apply the correction in the class header to ensure the bias consistency relation is upheld. Returns: Array of \(I_1^2\) values for each k. Return type: np.ndarray
Halo Power Module¶
-
class
PerturbedHalos.HaloPower.
HaloPower
(cosmology, mass_function, halo_physics, kh_vector, kh_min=0, verb=False)[source]¶ Class to compute the non-linear power spectrum from the halo model of Philcox et al. 2020.
The model power is defined as
\[P_\mathrm{model} = I_1^1(k)^2 P_{NL}(k) W^2(kR) + I_2^0(k,k)\]where \(I_p^q\) are mass function integrals defined in the MassIntegrals class, \(P_{NL}\) is the 1-loop non-linear power spectrum from Effective Field Theory and \(W(kR)\) is a smoothing window on scale R.
Parameters: - cosmology (Cosmology) – Instance of the Cosmology class containing relevant cosmology and functions.
- mass_function (MassFunction) – Instance of the MassFunction class, containing the mass function and bias.
- halo_physics (HaloPhysics) – Instance of the HaloPhysics class, containing the halo profiles and concentrations.
- kh_vector (np.ndarray) – Vector of wavenumbers (in \(h/\mathrm{Mpc}\) units), for which power spectrum will be computed.
Keyword Arguments: - kh_min – Minimum k vector in the simulation (or survey) region in \(h/\mathrm{Mpc}\) units. Modes below kh_min are set to zero, default: 0.
- verb (bool) – If true output useful messages througout run-time, default: False.
-
compute_one_loop_only_power
()[source]¶ Compute the one-loop SPT power from the linear power spectrum in the Cosmology class. This returns the one-loop power evaluated at the wavenumber vector specfied in the class initialization. When first called, this computes an interpolator function, which is used in this and subsequent calls.
Returns: Vector of 1-loop power \(P_\mathrm{1-loop}(k)\) for the input k-vector. Return type: np.ndarray
-
compute_resummed_linear_power
()[source]¶ Compute the IR-resummed linear power spectrum, using the linear power spectrum in the Cosmology class.
The output power is defined by
\[P_\mathrm{lin, IR}(k) = P_\mathrm{lin, nw}(k) + P_\mathrm{lin, w}(k)e^{-k^2\Sigma^2}\]where ‘nw’ and ‘w’ refer to the no-wiggle and wiggle parts of the linear power spectrum and \(\Sigma^2\) is the BAO damping scale (computed in the _prepare_IR_resummation function)
If already computed, the IR resummed linear power is simply returned.
Returns: Vector of IR-resummed linear power \(P_\mathrm{lin,IR}(k)\) for the input k-vector. Return type: np.ndarray
-
compute_resummed_one_loop_power
()[source]¶ Compute the IR-resummed linear-plus-one-loop power spectrum, using the linear power spectrum in the Cosmology class.
The output power is defined by
\[P_\mathrm{lin+1, IR}(k) = P_\mathrm{lin, nw}(k) + P_\mathrm{1-loop, nw}(k) + e^{-k^2\Sigma^2} [ P_\mathrm{lin, w}(k) (1 + k^2\Sigma^2) + P_\mathrm{1-loop,w}(k) ]\]where ‘nw’ and ‘w’ refer to the no-wiggle and wiggle parts of the linear / 1-loop power spectrum and \(Sigma^2\) is the BAO damping scale (computed in the _prepare_IR_resummation function)
Returns: Vector of IR-resummed linear-plus-one-loop power \(P_\mathrm{lin+1,IR}(k)\) for the input k-vector. Return type: np.ndarray
-
halo_power
(cs2, R, pt_type='EFT', pade_resum=True, smooth_density=True, IR_resum=True)[source]¶ Compute the non-linear halo-model power spectrum to one-loop order, with IR corrections and counterterms. Whilst we recommend including all non-linear effects, these can be optionally removed with the Boolean parameters.
This is similar to the ‘non_linear_power()’ function, but includes the halo mass integrals, and is the complete model of the matter power spectrum at one-loop-order in our approximations. Note that the function requires two free parameters; the smoothing scale R and the effective squared sound-speed \(c_s^2\), which cannot be predicted from theory. (Note that \(c_s^2<0\) is permissible).
For further details, see the class description.
Parameters: - cs2 (float) – Squared-speed-of-sound counterterm \(c_s^2\) in \((h^{-1}\mathrm{Mpc})^2\) units. (Unused if pt_type is not “EFT”)
- R (float) – Smoothing scale in \(h^{-1}Mpc\). This is a free parameter of the model. (Unused if smooth_density = False)
Keyword Arguments: - pt_type (str) – Which flavor of perturbation theory to adopt. Options ‘EFT’ (linear + 1-loop + counterterm), ‘SPT’ (linear + 1-loop), ‘Linear’, default: ‘EFT’
- pade_resum (bool) – If True, use a Pade resummation of the counterterm \(k^2/(1+k^2) P_\mathrm{lin}\) rather than \(k^2 P_\mathrm{lin}(k)\), default: True
- smooth_density (bool) – If True, smooth the density field on scale R, i.e. multiply power by W(kR)^2, default: True
- IR_resum (bool) – If True, perform IR resummation on the density field to resum non-perturbative long-wavelength modes, default: True
Returns: Non-linear halo model power spectrum \(P_\mathrm{halo}\) evaluated at the input k-vector.
Return type: np.ndarray
-
non_linear_power
(cs2, R, pt_type='EFT', pade_resum=True, smooth_density=True, IR_resum=True)[source]¶ Compute the non-linear power spectrum to one-loop order, with IR corrections and counterterms. Whilst we recommend including all non-linear effects, these can be optionally removed with the Boolean parameters. Setting (pt_type=’Linear’, pade_resum=False, smooth_density=False, IR_resum = False) recovers the standard halo model prediction.
Including all relevant effects, this is defined as
\[P_\mathrm{NL}(k, R, c_s^2) = [P_\mathrm{lin}(k) + P_\mathrm{1-loop}(k) + P_\mathrm{counterterm}(k;c_s^2)] W(kR)\]where
\[P_\mathrm{counterterm}(k;c_s^2) = - c_s^2 \frac{k^2 }{(1 + k^2)} P_\mathrm{lin}(k)\]is the counterterm, and IR resummation is applied to all spectra.
This computes the relevant integrals if they haven’t already been computed. The function returns \(P_\mathrm{NL}\) given smoothing scale R and effective squared sound-speed \(c_s^2\).
Parameters: - cs2 (float) – Squared-speed-of-sound counterterm \(c_s^2\) in \((h^{-1}\mathrm{Mpc})^2\) units. (Unused if pt_type is not “EFT”)
- R (float) – Smoothing scale in \(h^{-1}Mpc\). This is a free parameter of the model. (Unused if smooth_density = False)
Keyword Arguments: - pt_type (str) – Which flavor of perturbation theory to adopt. Options ‘EFT’ (linear + 1-loop + counterterm), ‘SPT’ (linear + 1-loop), ‘Linear’, default: ‘EFT’
- pade_resum (bool) – If True, use a Pade resummation of the counterterm \(k^2/(1+k^2) P_\mathrm{lin}\) rather than \(k^2 P_\mathrm{lin}(k)\), default: True
- smooth_density (bool) – If True, smooth the density field on scale R, i.e. multiply power by W(kR)^2, default: True
- IR_resum (bool) – If True, perform IR resummation on the density field to resum non-perturbative long-wavelength modes, default: True
Returns: Non-linear power spectrum \(P_\mathrm{NL}\) evaluated at the input k-vector.
Return type: np.ndarray
Counts Covariance Module¶
-
class
PerturbedHalos.CountsCovariance.
CountsCovariance
(cosmology, mass_function, halo_physics, mass_integrals, kh_vector, mass_bins, volume, kh_min=0, verb=False)[source]¶ Class to compute the covariance of cluster counts and the non-linear power spectrum using the halo model of Philcox et al. 2020
The model covariance is defined as
\[\mathrm{cov}_\mathrm{no\,SSC}(N_i, P(k)) = I_1^1(k) [ 2 {}_iJ_1^1(k) P_{NL}(k) W^2(kR) + ... ] + {}_iJ_2^0(k,k)\]where \(I_p^q\) and \({}_iJ_p^q\) are mass function integrals defined in the MassIntegrals class for mass bin i, \(P_{NL}\) is the 1-loop non-linear power spectrum from Effective Field Theory and \(W(kR)\) is a smoothing window on scale R. The ellipses refer to 1-loop bispectrum and trispectrum terms which are usually ignored.
\(N_i\) is defined as the number of halos in a mass bin defined by [\(m_{low,i}\), \(m_{high,i}\)]
There is an additional contribution from super-sample-covariance:
\[\mathrm{cov}_\mathrm{SSC}(N_i, P(k)) = V \sigma^2(V) {}_iJ_0^1 [ I_1^1(k) I_1^{1,1}(k) W^2(kR) + I_2^1(k) ]\]where \(\sigma^2(V)\) is the variance of the linear density field on scales with volume V.
Parameters: - cosmology (Cosmology) – Class containing relevant cosmology and functions.
- mass_function (MassFunction) – Class containing the mass function and bias.
- halo_physics (HaloPhysics) – Class containing the halo profiles and concentrations.
- mass_integrals (MassIntegrals) – Class containing the mass integrals.
- kh_vector (np.ndarray) – Vector of wavenumbers (in \(h/\mathrm{Mpc}\) units), for which power spectrum will be computed.
- mass_bins (np.ndarray) – Array of mass bin edges, in \(h^{-1}M_\mathrm{sun}\) units. Must have length N_bins + 1.
- volume – Volume of the survey in \((h^{-1}\mathrm{Mpc})^3\). The variance of the linear field will be computed for radius giving this volume
Keyword Arguments: - kh_min – Minimum k vector in the simulation (or survey) region in \(h/\mathrm{Mpc}\) units. Modes below kh_min are set to zero, default 0.
- verb (bool) – If true output useful messages througout run-time, default: False.
-
counts_covariance
(cs2, R, use_SSC=True, pt_type='EFT', pade_resum=True, smooth_density=True, IR_resum=True)[source]¶ Compute the full SSC+no-SSC covariance matrix of \(N_i, P(k)\) as defined in the class description. Whilst we recommend including all non-linear effects, these can be optionally removed with the Boolean parameters. Setting (pt_type=’Linear’, pade_resum=False, smooth_density=False, IR_resum = False) recovers the standard halo model prediction.
If use_SSC = False, then we only return the non-SSC covariance.
Parameters: - cs2 (float) – Squared-speed-of-sound \(c_s^2\) counterterm in \((h^{-1}\mathrm{Mpc})^2\) units. (Unused if pt_type is not “EFT”)
- R (float) – Smoothing scale in :math:h^{-1}`mathrm{Mpc}`. This is a free parameter of the model. (Unused if smooth_density = False)
Keyword Arguments: - use_SSC (bool) – Whether to include the super-sample covariance (SSC) terms, default: True
- pt_type (str) – Which flavor of perturbation theory to adopt. Options ‘EFT’ (linear + 1-loop + counterterm), ‘SPT’ (linear + 1-loop), ‘Linear’, default: ‘EFT’
- pade_resum (bool) – If True, use a Pade resummation of the counterterm \(k^2/(1+k^2) P_\mathrm{lin}\) rather than \(k^2 P_\mathrm{lin}(k)\), default: True
- smooth_density (bool) – If True, smooth the density field on scale R, i.e. multiply power by W(kR)^2, default: True
- IR_resum (bool) – If True, perform IR resummation on the density field to resum non-perturbative long-wavelength modes, default: True
Returns: Two-dimensional array of \(\mathrm{cov}(N_i,P(k))\) with shape (N_bins, N_k) for N_bins mass bins and N_k power spectrum bins.
Return type: np.ndarray


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Each turing machine can be specified by the five elements:
Many interesting properties of Turing Machines have been proven so far. For example, that each Turing Machine can be transformed into a Turing Machine with a tape that is cut-off on one side, and endless on the other side. Or that every Turing machine can be transformed into a Turing machine with set of symbols contains just two symbols.
A language is said to be 'Turing-complete', if for each functions that can be calculated with a Turing Machine, it can be shown that there is a program in this language that performs the same function. There are basically three approaches to proof that a language is Turing-complete. These are:
To achieve this, the set of symbols A is mapped onto the numbers 0 to n-1, where n equals the number of symbols, such that ainit maps onto zero. Likewise, the set of states S is mapped onto the numbers 0 to m-1, where m equals the number of states, such that sinit maps onto zero, and sfinal maps onto 1.
To simulate a Turing machine, we need an array with unlimited length to represent the tape, a index into that array representing the position of the head, and the current state. To program this in BF we will need to assign these to some memory locations. The position of the head will be stored in memory location head, and the current state in the memory location state. Of course, some additional temporary memory locations will be needed. Using the terminology introduced on the page An introduction to programming in BF, we need a program of the following form:
(some code which given the state and the cursymbol
assigns a value to newstate, newsymbol, and newhead)
setarray(base,1,0,newhead,newsymbol)
zero(cursymbol)
zero(newsymbol)
zero(head) move(newhead,head,t1)
zero(state) move(newstate,state,t1)
IsOne(state,t1)
Not(t1,t2,t3)
map(state,head,cursymbol, i,j,k,l,m, newstate,newhead,newsymbol)Where, given the tupple f(si,aj), k is the number representing the new state, l is the number representing the new symbol, and m is equal to 1 if the movement is right and equal to 0 if the movement is left. The procedure map is defined as follows:
map(state,head,cursymbol, astate,asymbol,anewstate,anewsymbol,movement, newstate,newhead,newsymbol) = copy(state,t1,t2) const(t2,astate) Equal(t1,t2,t3,t4,t5) if(t3) copy(cursymbol,t1,t2) const(t2,asymbol) Equal(t1,t2,t3,t4,t5) if(t3) const(newstate,anewstate) const(newsymbol,anewsymbol) copy(head,newhead,t1) ifelse(movement,t1) inc(newhead) else(movement,t1) dec(newhead) endelse(t1) endif(t3) endif(t3)In this code the expression const(v,c) stands for the piece of code that fills the memory location v with the value c. Now, we only need to assign real values to the variable representing the memory locations to arrive at the final BF program executing the given Turing machine. Note that memory location assigned to base should be larger than all other memory locations used.
|
this fully documented BF program written by Daniel B. Cristofani. |
A Universal Turing Machine (UTM) is a Turing machine that can simulate some Turing-complete computational model. By giving a BF program which simulates a particular UTM, we proof that BF is Turing-complete. The UTM that we implement here is taken from from Yurii Rogozhin's article Small universal Turing machines, in Theoretical Computer Science, November 1996 (volume 168 pgs 215-240). This UTM simulate a Turing-complete class of tag-systems. A tag-system transforms strings over an alphabet A = {a[1],a[2],...,a[n], a[n+1]} as follows: a positive integer m is chosen, and so is a function P that maps each a[i] for 1<=i<=n to a string P(a[i]) over the alphabet A. Now:
The input for this Turing machine is mildly complex, and there is no error checking.
It meets the criteria above; and when applied to the initial string a[2]a[1]a[1] it gives:
a[2]a[1]a[1] a[1]a[3]a[3]a[1] a[3]a[1]a[3]a[3]a[2]a[1]a[4] a[3]a[3]a[2]a[1]a[4]a[3]a[3] a[2]a[1]a[4]a[3]a[3]a[3]a[3] a[4]a[3]a[3]a[3]a[3]a[3]a[3]a[1] a[3]a[3]a[3]a[3]a[3]a[1]and then it's done.
Now, the encoding:
a[1] is 1 a[2] is<PHONE_NUMBER>1 a[3] is<PHONE_NUMBER>1111111 a[4] is<PHONE_NUMBER>11111111111 P(a[1]) is b1 b111111111111111111111b b1b b11111111111b b11111111111111111b b1111111111111111 P(a[2]) is b1 b1b b11111111111111111b b111111 P(a[3]) is b1 b11111111111111111b bthe initial string is<PHONE_NUMBER>1c1c1
and so the whole input is
b1 b11111111111111111b b b1 b1b b11111111111111111b b111111 b1 b111111111111111111111b b1b b11111111111b b11111111111111111b b1111111111111111 b<PHONE_NUMBER>1c1c1which when run together for input to the Turing machine becomes
b1b11111111111111111bbb1b1bb11111111111111111bb111111b1b111111111111111111111bb1bb11111111111bb11111111111111111bb1111111111111111b11111111111c1c1
| 11<L1 | 210R2 | 311R3 | 410R4 |
| 1b>R1 | 2b>L3 | 3b<R4 | 4bcL2 |
| 1>bL1 | 2><R2 | 3>bR3 | 4><R4 |
| 1<0R1 | 2<>L2 | 3< H | 4< |
| 10<L1 | 201L2 | 30cR1 | 40cL2 |
| 1c0R4 | 2cbR2 | 3c1R1 | 4cbR4 |
The minimal test case b1b1bbb1c1c11111 represents the tag-system where P(a[1]) = a[1]a[1] and P(a[2]) = STOP, applied to the string a[1]a[1]a[2]. This runs for 518 steps of the Turing machine, exercising all 23 Turing machine instructions, before halting with the output string a[1].
+++>++>>>+[>>,[>+++++<[[->]<<]<[>]>]>-[<<+++++>>-[<<---->>-[->]<]] <[<-<[<]+<+[>]<<+>->>>]<]<[<]>[-[>++++++<-]>[<+>-]+<<<+++>+> [- [<<+>->- [<<[-]>>- [<<++>+>- [<<-->->>+++<- [<<+>+>>--<- [<<->->- [<<++++>+>>+<- [>-<- [<<->->- [<<->>- [<<+++>>>-<- [<<---->>>++<- [<<++>>>+<- [>[-]<- [<<->>>+++<- [<<->>>--<- [<<++++>+>>+<- [<<[-]>->>++<- [<<+++++>+>>--<- [<->>++< [<<->>- ]]]]]]]]]]]]]]]]]]]]]]<[->>[<<+>>-]<<<[>>>+<<<-]<[>>>+<<<-]]>>] >[-[---[-<]]>]>[+++[<+++++>--]>]+<++[[>+++++<-]<]>>[-.>]
The Universal Register Machine is a machine with a fixed number of characters, and it supports the following commands:
(a2;s3)3.
(a4;a5;s2)2; ((a2;s4)4; s3; (a1;a4;s5)5; (a5;s1)1)3.
There is almost a one-to-one mapping from URM to BF. The an expression maps to +, the sn expression maps to -, and the (x)n expression maps to [x], of course preceded with the right amouth of > and < to move to the indicated memory location. The translation of the above two URM programs to BF are:
>>>[<+>-]<<<
>>[>>+>+<<<-]>[>[<<+>>-]<->>[<<<<+>>>+>-]<<<<[>>>>+<<<<-]>>]<<<
It is possible to make context free grammars for both BF and URM, such that matching parse trees indicate equivalent programs. Such a grammar is given below:
| URM | BF |
| root = S1. | root = S1 |
| Sn = an | Sn = + |
| Sn = sn | Sn = - |
| Sn = Sn ; Sn | Sn = Sn Sn |
| Sn = ( Sn )n | Sn = [ Sn ] |
| Sn = Sn+1 | Sn = > Sn+1 < |
| Sn = Sn-1 | Sn = < Sn-1 > |
Using this mapping, one can create another UTM in BF from the above mentioned UTM in URM.
Still, I feel that BF is far more elegant than URM, because it gives you more with less symbols. BF only needs the symbols "+", "-", "<", ">", "[", and "]", whereas URM needs "a", "s", ";", "(", ")", ".", and "0" to "9". Although, I have to admit, that BF programs will in general be longer than the equivalent URM program, and in most cases also more cryptic.


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Google Maps now will speak for you when you’re asking for directions while traveling
We’ve heard a lot of Google Maps’ new features recently and here’s another one to join the family! Google has now integrated one of its useful services which is Google Translate into the navigation app. It is said to bring a lot of conveniences while you’re traveling in another country which speaks a different language.
For example, the app now will help you to translate the name of a place from your native language to another foreign language. It will also speak the name out loud using Text-to-Speech for the locals to understand. It comes really handy when you’re asking for directions to a certain place when you don’t know how to speak their language.
The update will be rolling out this month on both iOS and Android. It will support 50 languages at launch and Google said there will be more coming soon.
Let us know what you think about this new feature on Google Maps! Stay tuned for more news on TechNave.com.


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A become-the-largest style game built entirely using JavaScript and canvas. The goal is to navigate the field and absorb smaller amoebas until your amoeba is the largest (or last remaining), but you have to sacrifice a little bit of your own mass to propel yourself. It uses a custom built physics engine to determine the absorption rate of each amoeba, and a quadtree for efficient collision detection.
WaveForm is a single page website built using React and Redux, based on SoundCloud (it's also the first one I ever built). It allows users to upload audio files subscribe to other users' uploads. It uses AWS S3 to store user tracks and album art, and comes equipped with fully developed music player capabilities, including queueing, drag and drop queue reorganization, and uninterrupted playback throughout site navigation.
StrongORM is an Object Relational Mapping (ORM) system. It operates on SQLite, interfacing with the database through the SQLite3 gem. Inspired by ActiveRecord from rails, StrongORM provides a connection to your database through representational Objects. These objects (models) can represent either entire tables or individual rows. This allows for quick and easy interaction with your database, avoiding explicit SQL queries and bloated code.
A full stack web-development program with < 3% acceptance rate. Curriculum includes Rails, SQL, JS, React, Redux, algorithms, and design patterns. Emphasizes best practices and pair-programming exercises
GPA: 3.54


ExecuteGuard Class
Definition
Line
12
of
spring/Action.cm
Constructors & Destructor
public
nothrow
ExecuteGuard
(
Diagram
& diagram_)
public
~ExecuteGuard
()
Member Variables
private
Diagram
&
diagram
Constructor& Destructor Details
ExecuteGuard Constructor
public
nothrow
ExecuteGuard(
Diagram
& diagram_)
Definition
Line
14
of
spring/Action.cm
~ExecuteGuard Destructor
public
~ExecuteGuard()
Definition
Line
17
of
spring/Action.cm


Welcome to Survey Portal
Ask one person for feedback, and it's hard to know whether they represent the majority or minority. Ask a
hundred, though, and you'll start to see a clearer picture and distinct trends.
Today, it's easier than ever to create and distribute a survey that collects exactly the information you
need to
make confideyesnt choices. Whether you're designing a new product, improving your site, or just wondering
whether people prefer literal apples or oranges.
If you're thinking about survey-building, you are in the right spot.
Survey Portal App provide a easy way to host your own surveys and collect responces all arroud the
world.
So, what are waiting for explore the world of surveys with us now.
**Use the navigation bar up top for using this app**


This tool summarizes a raster based on areas (zones) defined by the first input layer.
Some example applications include the following:
If Use current map extent is checked, only those features in the input layer and the layer to be summarized that are visible within the current map extent will be analyzed. If unchecked, all features in both the input layer and the layer to be summarized will be analyzed, even if they are outside the current map extent.
The layer that defines the boundaries of the areas, or zones, that will be summarized.
The layer can be a raster or feature data. For rasters, the zones are defined by all locations in the input that have the same cell value. The areas do not have to be contiguous.
This is the attribute of the layer that will be used to define the boundaries of the areas.
For example, suppose the first input layer defines the management unit boundaries, with attributes that define the region, the district, and the parcel ID of each unit. You also have a raster layer defining a biodiversity index for each location. With the field you select, you can decide to calculate the average biodiversity at local, district, or regional levels.
The raster cells in this layer will be summarized by the areas (zones) that they fall within.
Once you choose a layer to summarize, you can optionally calculate statistics of any numerical attribute of the points, lines, or areas within the input area layer.
The available statistics types when the selected field is integer are Average, Majority, Maximum, Median, Minimum, Minority, Range, Standard deviation, Sum, and Variety.
If the field is floating point, the options are Average, Maximum, Minimum, Range, Standard deviation, and Sum.
If you choose to ignore missing values, only the cells that have a value in the layer to be summarized will be used in determining the output value for that area. Otherwise, if there are missing values anywhere in an area, it is deemed that there is insufficient information to perform statistical calculations for all the cells in that zone, and that area will receive a null (NoData) value in the output.
The name of the layer that will be created in My Content and added to the map. The default name is based on the tool name and the input layer name. If the layer already exists, you will be prompted to provide another name.
You can specify the name of a folder in My Content where the result will be saved using the Save result in drop-down box.


There is supposed to be an example drawing here, but it's not important.
This is some text under the canvas


| 30 | (A) | witħ a kankire vn-clene clotherede to-gedir |
| 30 | (C) | As a kankur vnclene . enclyned he hadde |
| 30 | (D) | As a kancre vnclene enclynid hid had |
| 30 | (E) | as a canker vn-clene . enclosyd it hadde . |
| (Ex) | ---- no text ---- | |
| 30 | (L) | so a canker vnclene hit cloched to-gedres |
| 29 | (P) | Als a kankyr vnclene . it clunchyd to-gedyr |
| 30 | (U) | A cancre vnclene / enclyned he had |
| (V) | ---- no text ---- |


The following methods are implemented to evaluate how sensitive the results of a meta-analysis are to potential bias in meta-analysis and to support Schwarzer et al. (2015) <doi:10.1007/978-3-319-21416-0>, Chapter 5 "Small-Study Effects in Meta-Analysis": - Copas selection model described in Copas & Shi (2001) <doi:10.1177/096228020101000402>; - limit meta-analysis by Rücker et al. (2011) <doi:10.1093/biostatistics/kxq046>; - upper bound for outcome reporting bias by Copas & Jackson (2004) <doi:10.1111/j.0006-341X.2004.00161.x>.
| Version: | 0.3-2 |
| Depends: | meta (≥ 4.9-0) |
| Published: | 2017-12-06 |
| Author: | Guido Schwarzer [aut, cre], James R. Carpenter [aut], Gerta Rücker [aut] |
| Maintainer: | Guido Schwarzer <sc at imbi.uni-freiburg.de> |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| URL: | https://github.com/guido-s/metasens http://meta-analysis-with-r.org |
| NeedsCompilation: | no |
| Materials: | NEWS |
| In views: | ClinicalTrials, MetaAnalysis |
| CRAN checks: | metasens results |
| Reference manual: | metasens.pdf |
| Package source: | metasens_0.3-2.tar.gz |
| Windows binaries: | r-devel: metasens_0.3-2.zip, r-release: metasens_0.3-2.zip, r-oldrel: metasens_0.3-2.zip |
| OS X binaries: | r-release: metasens_0.3-2.tgz, r-oldrel: metasens_0.3-2.tgz |
| Old sources: | metasens archive |
Please use the canonical form https://CRAN.R-project.org/package=metasens to link to this page.


{{ content }}
Recent Updates
- Shivang Bharti from our lab was chosen as the 2nd runner up by IEEE CASS UG Project Award committee for his BTech project titled "A Light-weight Software Defined Networking Architecture for DebriNet 3."
- Sarath Babu joined as a Research Scientist at Iowa State University, USA
- Abhishek Chakraborty joined as a Postdoctoral Fellow at University of California, San Diego, USA


For more details, please refer to Soul of Eden.
．Simplify the game
The original game is complicated. Since our main
goal is to show our AI’s
feasibility, we simplify the game. The simplified game is as following.
．Destroy the opposite’s castle
In the given time, players need to
destories the opposite’s
castle. The one who destroy the opposite’s castle wins the game.
If none of the castles is destroyed in the time limit, the game is considered to be draw.
．Game Cards
There are 3 kinds of cards in the game.
For every 4 seconds, each player should choose one kind of cards to play.
After playing 30 cards, the players stop playing cards and wait for the final result.
240 seconds
30
2800HP
Medium attack power
Fast attack speed.
621HP
Low attack damage
Block the attack from the enemy’s archer
162HP
High attack damage
The main attacker in the game,
usually protected by tanks
162HP
Medium attack damage
Buff nearby teammates.
Each player chooses a type of card to play every 4 seconds.
Each player should stop playing cards after 120 seconds.
The game continues until one of the castles is destroyed or the time limit exceeds.
Destroy the enemy’s castle.
If none of the castles is destroyed in the time limit, the game is considered to be draw.
3 kinds of cards we can use and 25 positions we can put.
-> Therefore, a behavior $b$ is formed by the card we use and the position we put.
Denote $c \in \{0,1,2\}$ as the card and $p \in \{0,1,...,24\}$as the position.
$b = 3 \times c + p$, $b \in \{0,1,2,...,74\}$.
We then use $b$ as the format of our training data.
    We let statistics model and random model play over 3,000 games and the statistics model have
more than 80%
winning rate, meaning that it is superior than the random model very much.
    We let RNN models play with the statistics model. Both of the models choose the best behavior they think as the decision, and therefore the game is deterministic. The result is that all of the RNN models defeat the statistics model, showing that RNN models are better than statistics model.
    We also let the two versions of RNN models play with each other. The result shows that their winning rates are nearly equal.
In the RNN model, we can decide the number of layers to stack the cells. Here we choose 2 and 4. The training curve is like the graph.
    The statistics model performs better than random model, and the RNN models outperforms the statistics model.
    Version 1 and version 2 RNN models have similar performance.
    The model that uses 4 layers of cells leads to a lower loss than the model that uses 2 layers of cells.
    Since we have some basic models now, we can use them to generate training data that has higher
quality.
We believe that the model could perform better if we use higher quality data.
    In version 2 of RNN model, we can try to use more complicated mapping method to map the 2 inputs into a vector. Maybe the version2 does not work well since the mapping is too easy.
Wei-Chung Liao
<EMAIL_ADDRESS>Chun-Wei Chen
<EMAIL_ADDRESS>Po-Yao Chen
B02902071@ntu.edu.tw


Remember what you know
"Remember what you know."
"Remember what you know."
Finally rolled back in town after 2am from Ohio Linux Fest 2009. Saw some amazing speakers and had a lot of fun learning about how free and open technology IS the future.
I happened to win a Neuros OSD device as a door prize. This morning I hooked one side of it to my TV and the other to my home network. Instantly it found all my shared files (mostly my MP3 library). After poking around the wiki site I found that I could access it through the network from another computer. "Sounds like fun", I thought. After using telnet to connect, here's what I found:
That's right, it's Linux! The next step is to get a web server running on it so that I can program it remotely (like from any internet enabled device) to record my TV/DVDs. There's countless other add-ons that can be loaded, and that's the beauty of it. Because it's Linux, I can add, remove, or change anything I care to. Sure I have to figure it out, but honestly, that's as much fun as actually using it.
This device is exemplary of why I love FOSS. I don't really care if it's Linux, I care that it's open. I can take this thing apart, refactor the software, and make it do things that the manufacturer did not imagine. I mean, think about it. How much does a DVR cost, and the monthly cost? Do you get to keep your recorded programs? Can you add storage? Do you get free upgrades? Can you export your recorded shows to your portable media player, or your computer, or your website? This device does all that, and, because it's open source, I can make it do it any way I want. Or I can find someone else who has added features and take their work and use it on my device.
Open source is about freedom and creativity. I recently dug out my Legos. They have got to be my favorite toy. They are a great example of an open system. Sure, I can follow the 44-step instructions and have an exact replica of the castle shown on the outside of the box. But I can also take as little or as much of those instructions I want and use the pieces to craft anything else. The nature of Legos is to provide a system by which any number of objects can be constructed. Freedom and creativity.
Besides the fact that I did not have many action figures growing up, the ones I did have weren't my toy of choice. I could build an action figure out of Legos, sure it's not going to look just like my Snake Eyes G.I. Joe, but that's not the point. With an G.I. Joe, I don't get a choice. Sure it's still play, and it got the job done, but G.I. Joe was never as fun as Legos. I think the constructive toys I had growing up have put me in a mindset that harmonizes with Open Source, maybe not.
 Thanks to Ohio Linux Fest 2009 for perspective.
-Nate


Before Change
else:
print(("* %s +" % author).encode("utf-8"))
print(
A total of %(count)d people contributed to this release.
People with a "+" by their names contributed a patch for the first time.
% dict(count=len(authors)))
print ("\nNOTE: Check this list manually! It is automatically generated "
"and some names\n may be missing.")
After Change
authors.sort(key=name_key)
// Print
stdout_b.write(b
Authors
=======
This release contains work by the following people (contributed at least
one patch to this release, names in alphabetical order):
)
for author in authors:
if author in all_authors:
stdout_b.write(("* %s\n" % author).encode("utf-8"))
else:
stdout_b.write(("* %s +\n" % author).encode("utf-8"))
stdout_b.write((
A total of %(count)d people contributed to this release.
People with a "+" by their names contributed a patch for the first time.
% dict(count=len(authors))).encode("utf-8"))
stdout_b.write(("\nNOTE: Check this list manually! It is automatically generated "
"and some names\n may be missing.\n").encode("utf-8"))
//------------------------------------------------------------------------------
// Communicating with Git
//------------------------------------------------------------------------------


The spectre of Cameron Diaz hangs heavily over "Lost & Found," and not just because the film climaxes with David Spade rocking out with a version of Neil Diamond's "Brother Love's Travelling Salvation Show" that outdoes Diaz's tuneless rendition of "I Just Don't Know What To Do With Myself" in "My Best Friend's Wedding.
Long before that unnerving sight, anyone who went to the movies last summer will recognize "Lost" for what it is: a diluted variation on Diaz's blockbuster "There's Something About Mary." Instead of bodily fluids in hair, "Lost" offers dog excrement being smeared on the face; in place of the now-infamous zipper gag, we get Spade trying to conceal his naked figure in an apron after losing big in a strip poker game.
For the under-12 crowd who couldn't persuade Mom and Dad to rent "Mary" for them, this might serve as a decent substitute. But anyone who's not a dyed-in-the-wool Spade fan might be crying "Just Shoot Me" well in advance of the closing credits - which, by the way, try to do for Deee-Lite's "Groove is in the Heart" what "Mary" did for the Foundations' "Build Me Up Buttercup."
Spade, with customary smirks intact, plays Dylan Ramsey, a bistro owner who spends considerably more time trying to put the make on comely French neighbor Lila (Sophie Marceau) than he does putting out kitchen fires and dealing with customers.As part of his plot to catch Lila's eye, Dylan kidnaps her beloved dog Jack, and when Lila becomes distraught over her chien's disappearance, Dylan is right there with a shoulder to cry on.
Unfortunately, it's Dylan's turn to weep when the voracious Jack swallows a diamond ring Dylan was holding on to for a friend. And the tears just keep on coming as one of Dylan's employees, the relentlessly jolly Wally (Artie Lange) decides to turn himself into a clone of the boss.
Lange, in a part obviously designed to position him as a replacement for the late Chris Farley (Spade's co-star in "Tommy Boy" and "Black Sheep"), comes off as merely a pale imitation; say what you will about Farley, but he had considerably more bluster and gusto than this new model. As for Marceau, she's adorable and earned every franc of her paycheck.
But the primary fun here comes from an unbilled cameo by Jon Lovitz as a "certified dog whisperer" Dylan enlists in the hopes of retrieving the ring. To call the rest of the humor in "Lost & Found" hit or miss would be kind.
James Sanford
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


Information Exchange prototypes {{releaseVersion}}
{{releaseVersion | log }}Alpha
- Allocations Academies
- Allocations Academies MAT's
- Allocations Academies SAT's
- Allocations AEB digital
- Dashboard 1
- Dashboard 2
- Dashboard 3
- Sub-contractors
- Subcontractor 2 Sprint Guatemala
- Subcontractor 3
- Subcontractor 4 Sprint Havana
- Subcontractor 5 Sprint Islamabad
- Subcontractor 6 Sprint Jakarta
- Subcontractor 7 Sprint Madrid
- Subcontractor Live
- Subcontractor MVP
- Subcontractor second journey
- Subcontractor after MVP
- Subcontractor May
- Subcontractor June
Allocations
Dashboards
Subcontractors
After MVP includes: pagination, declaration history, ability to use last declaration details for a new declaration.
How does the user know what year they are declaring for - is this what the business needs.
Can the user declare at any time now that the digital version is available?
- SAT
- SAT 2
- MAT 1
- MAT 2
- MAT 3
- Special GAG
- Document Exchange MAT
- Document Exchange SAT's
- Document Exchange SAT's 2
Information Exchange
Sprint three 2 May 2018
Sprint four 16 May 2018
- Document Exchange SAT 4
- Document Exchange MAT 4
- Document Exchange SAT 5
- PE1
- Adult Allocations David
- Adult Funding Mel
Sprint one private beta June 2018
- Document Exchange SAT 4
- Document Exchange MAT 4
- Document Exchange SAT 5
- PE public
- PE SFS
- Adult Allocations David
- Adult Funding Mel
Sprint one private beta iterations
Sprint three private beta iterations
- External upload for a MAT
- External upload for a SAT
- Adult for FE and ILP
- Adult for Roop
- PE public google Journey 1
- PE public google Journey 2
- PE .GOV page
- PE public skills search
- Adult funding
- PE public for Greta
- Funding claims - 16 to 19
- Admin Upload 2
- Announcements
Skills Funding Service
PE and Sport Premium - September 2018
- Journey start points on .gov
-
- Find an organisation
- Journey split
- Shirland primary school
- Derbyshire
- Derbyshire maintained
- St. Josephs - search results
- St. Josephs - search results - Rotherham
- St. Josephs search results - Rotherham and Academy
- St. Josephs Catholic Primary School
Concepts for consideration
Other resources


A personal infrastructure experiment
If you want in, the pre-requisite is that you know someone with an inflo.ws email id and they know you well enough. Just get in touch with them.


smp.cp_model¶
-
smp.
cp_model
(epsilon, particles, rho_a, rho, g, rho_r, b, u)[source]¶ Continuous peeling model of Crounse (2000)
Computes the local peeling flux from the continuous model of Crounse (2000)
- Parameters
- epsilonfloat
Continuous peeling model calibration factor (–).
- particleslist of single_particle_model.Particle objects
Iterable list of dbm class objects describing each dispersed phase.
- rho_afloat
Local density of ambient fluid outside plume (kg/m^3).
- rhofloat
Local density of plume fluid (kg/m^3)
- gfloat
Acceleration of gravity (m/s^2).
- rho_rfloat
Model reference density (kg/m^3).
- bfloat
Local plume half-width (m)
- ufloat
Local plume fluid velocity (m/s)


UKCloud Limited (“UKC”) and Virtual Infrastructure Group Limited (“VIG”) (together “the Companies”) – in Compulsory Liquidation
On 25 October 2022, the Companies were placed into Liquidation with the Official Receiver appointed as Liquidator and J Robinson and A M Hudson simultaneously appointed as Special Managers to manage the liquidation process on behalf of the Official Receiver.
Further information regarding the Liquidations can be found here: https://www.gov.uk/government/news/virtual-infrastructure-group-limited-and-ukcloud-limited-information-for-creditors-and-interested-parties
Contact details:
For any general queries relating to the Liquidations please email<EMAIL_ADDRESS>For customer related queries please email<EMAIL_ADDRESS>For supplier related queries please email<EMAIL_ADDRESS>Private Cloud Storage Service Scope
About the service
This document describes the boundaries of the Private Cloud Storage service, along with the responsibilities of both you and UKCloud to facilitate the installation and ongoing use of the service.
Our Private Cloud Storage service is a single‑tenant (private cloud) storage infrastructure where your storage needs are hosted either in one of our data centres, to gain the benefits of our Assured and Elevated cloud platforms; or in your Crown Hosting Data Centre (CHDC).
This service offers an increase in both performance consistency and data security over traditional public cloud storage options.
We can provide Private Cloud Storage on an all-inclusive basis, or you can provide your own hardware, which we'll maintain on your behalf.
Capturing your requirements
Your Cloud Architect will capture:
Your end-to-end solution, including your backup and connectivity needs
A forecast of your growth
Your requirements for either an All-Inclusive, UKCloud hosted, or Crown Hosting Data Centre (CHDC) hosted solution
Any deadlines we need to meet
Designing your solution
Your Cloud Architect will design your solution based on your needs and will confirm that the design meets your requirements.
When you have accepted the design and provided a purchase order, we'll start to plan the installation, including allocating space in our data centres if applicable.
A project manager will be assigned to manage the install, testing and operational hand over of your service.
Design options
Your storage solution can be:
In either or both of our two data centres - Farnborough and Corsham, or in a CHDC
Connected to your compute environment in either our Assured OFFICIAL or Elevated OFFICIAL security domain
Part of a Platform as a Service (PaaS) environment
Independent of any other UKCloud product
Connected via the internet, HybridConnect, Janet, MPLS, HSCN, PSN or Secure Remote Access
Installation
Your project manager will coordinate the build activities, work with your hardware installers and carry out end-to-end testing of your storage solution.
During the installation, we will set up monitoring tools on your storage environment so that we can maintain your service once it has gone live.
Your storage solution will be handed over to you when your project manager can confirm that the testing has proved successful and that you can configure your storage solution to your requirements.
At this time, your storage solution will be considered live.
Maintaining your environment
We'll monitor the end-to-end solution for alarms, including your hardware issues and failures.
We'll perform routine maintenance and diagnostics and will liaise with your hardware maintenance provider where necessary.
If necessary, we'll co-ordinate the swapping out of any failed hardware and notify you of any service-affecting maintenance through our change control and notification procedures.
As your storage needs grow, we'll work with you to coordinate the installation of any additional hardware and network requirements.
Your responsibilities
Your All-Inclusive responsibilities
Providing an initial forecast of your needs and regularly updating us to cover the minimum term, ensuring we can provision your requirements when needed
Managing the performance of your workload
Your UKCloud Hosted responsibilities
Providing an initial forecast of your needs and regularly updating us to cover the minimum contract term, ensuring we can provide data centre capacity
Agreeing to our hardware design
Purchasing the hardware and network infrastructure to an agreed specification
Arranging a service and maintenance contract for your hardware
Arranging the installation of your hardware and associated software
Arranging a software agreement for software patches and releases
Managing the performance of your workload
Agreeing with us on how to deal with hardware failures and associated removal and/or disposal
Performing capacity planning and working with us to plan upgrades
Raising service requests through the My Calls section of the UKCloud Portal when you need configurations implemented
Raising incident tickets if you experience any issues with your service
Giving us time to plan the installation of any additional hardware
Supplying us with all network switches and cabling to connect to your storage environment - or we can source these for you
Your CHDC Hosted responsibilities
Arranging for CHDC capacity for your hardware
Providing access for UKCloud engineers to install network connectivity
Agreeing to our hardware design
Purchasing the hardware and network infrastructure to an agreed specification
Arranging a service and maintenance contract for your hardware
Arranging for connectivity between the CHDC and the UKCloud platform
Arranging the installation of your hardware and associated software
Arranging a software agreement for software patches and releases
Providing access for UKCloud engineers to manage your environment
Managing the performance of your workload
Agreeing with us on how to deal with hardware failures and associated removal and/or disposal
Performing capacity planning and working with us to plan upgrades
Raising Service Requests through the My Calls section of the UKCloud Portal when you need configurations implemented
Raising incident tickets if you experience any issues with your service
Giving us time to plan the installation of any additional hardware
Supplying us with all network switches and cabling to connect to your storage environment - or we can source these for you
Our responsibilities
Our All-Inclusive responsibilities
Designing a solution that meets your needs
Ensuring the solution is installed, tested and ready for service before handing over to you
Monitoring your environment and running diagnostics
Fixing any issues that arise in your environment
Applying software patches and upgrades for you
Providing you with visibility of capacity utilisation to ensure capacity planning can be effectively performed
Attending any required service reviews and project progress calls that you need
Notifying you of any maintenance windows and agreeing a suitable time to implement
Our UKCloud Hosted and CHDC Hosted responsibilities
Working with you to design a solution that meets your needs
Ensuring all UKCloud installed hardware is tested and ready for service before handing over to you
Monitoring your environment and running diagnostics
Fixing any issues that arise in your environment
Applying software patches and upgrades for you
Liaising with your hardware maintainers and allowing them supervised access if required
Providing you with visibility of capacity utilisation to ensure capacity planning can be effectively performed
Managing any additional hardware installation
Attending any required service reviews and project progress calls that you need
Notifying you of any maintenance windows and agreeing a suitable time to implement
What we are not responsible for
We will not provide you with access to any management applications that we use to run and maintain your storage environment.
We will not supply you with root access to your hardware as your hardware will be maintained by us; we'll work with you to configure it to your needs.
To progress further
For more information, see the Private Cloud Storage Service Definition. Contact your Service Delivery Manager to request further information or to place an order.
Feedback
If you find a problem with this article, click Improve this Doc to make the change yourself or raise an issue in GitHub. If you have an idea for how we could improve any of our services, send an email to feedback@ukcloud.com.


public class CitationCore
extends java.lang.Object
Brief Description:
This project will explore the concept of predicting future citations based
on a citation history of a given paper. The project relies on the initial
research of Wang, Song, and Barabasi, which is outlined in their paper titled:
"Quantifying Long-Term Scientific Impact" published in "Science 342, 127 (2013)".
The prediction is based on three different qualities:
1. Preferred attachment
2. Age Decay
3. Fitness
These three qualities are represented across three variables (The WSB Triple: Wang-Song-Barabási)
1. (mu) - "indicates immediacy, governing the time for a paper to reach its citation peak (Science pg 128)"
2. (sigma) - "is longevity, capturing the decay rate (Science pg 128)"
3. (lambda) - relative fitness, which is related to '' the paper's fitness which "captures
the inherent differences between papers, accounting for the perceived novelty and
importance of a discovery. (Science pg 128-129)"
This Java program will solve the WSB triple by using the general math developed by Dr. Parks to implement the Newton-Raphson method of numeric analysis applied to the three non-linear equations found in the WSB paper. The WSB Triple along with equation #3 on page 129 of the WSB paper will be used to predict future citations of a paper based on a segment of the paper's citation history.
This class makes use of several packages of the Apache Commons Library (Apache License, V2.0): http://commons.apache.org/
Specifically:
Math.Linear (RealMatrix, LUDecomposition, DecompositionSolver, MatrixUtils)
Math.Distribution (NormalDistributation: CDF and PDF functions)
CSV.CSVRecord
CSV.CSVParser
Note: the commons.csv package is part of the Sandbox package and therefore is considered in beta with no official releases.
this class uses the most recent build to extract data from a tabbed delimited csv file.
The graphs are all done using the jmathplot library (BSD 3-clause License), which can be found at:
http://code.google.com/p/jmathplot/
License:
Copyright 2014 Josiah Neuberger & William Etcho
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
| Modifier and Type | Class and Description |
|---|---|
class |
CitationCore.CitationCoreTest
This is a basic test class that allows for the creation of various test, which can be
added to the 'tests' variable structure for presentation to the user during execution.
|
| Constructor and Description |
|---|
CitationCore() |
| Modifier and Type | Method and Description |
|---|---|
double |
getLambda(double[][] data,
double mu,
double sigma,
double m,
double t,
double n)
Calculate lambda based on a solution found in the Newton-Raphson method for mu and sigma.
|
org.math.plot.Plot2DPanel |
graphWSB(double[][] data_in_days,
double m,
org.math.plot.Plot2DPanel plot,
java.lang.String graphTitle,
java.lang.String lineLegend,
java.util.ArrayList<java.util.LinkedHashMap<java.lang.String,java.lang.Double>> wsbSolutions,
boolean showGraph,
javax.swing.JFrame frame)
This function will take a list of WSB solutions and graph them.
|
static void |
main(java.lang.String[] args) |
static java.util.ArrayList<java.util.LinkedHashMap<java.lang.String,java.lang.Double>> |
newtonRaphson_ConvergenceTest(double[][] data,
double step,
double m)
This function runs the Newton-Raphson function on an interval from .1 to 10 returning a list of
all the unique solutions.
|
java.util.LinkedHashMap<java.lang.String,java.lang.Double> |
newtonRaphson(double[][] data,
double mu,
double sigma,
double m)
This function implements the algorithm designed by Josiah Neuberger and William Etcho used to solve for a WSB solution.
|
void |
printList(java.util.LinkedHashMap<java.lang.String,java.lang.Double> l)
This function will print a list containing the calculated values for the Newton-Raphson method in
a formated way that is easy to read.
|
static void |
printMatrix(java.util.ArrayList<java.util.ArrayList<java.lang.Double>> l,
java.lang.String[] header)
Prints the citation history stored in 'l' in a formated way.
|
static java.lang.String |
toString(double[][] data)
Convert citation history to a String object.
|
public static void main(java.lang.String[] args) throws java.io.IOException
java.io.IOException
public org.math.plot.Plot2DPanel graphWSB(double[][] data_in_days, double m, org.math.plot.Plot2DPanel plot, java.lang.String graphTitle, java.lang.String lineLegend, java.util.ArrayList<java.util.LinkedHashMap<java.lang.String,java.lang.Double>> wsbSolutions, boolean showGraph, javax.swing.JFrame frame)
data_in_days
- The citation data distributed mostly even in days (call fixdata function if data is in years).m
- The average number of new references in each new paper for a journal.plot
- The plot you would like the WSB solution plotted to.graphTitle
- The title to display on the JPanel.lineLegend
- The title of this curve.wsbSolutions
- The list of WSB solutions to graph.showGraph
- Display the graph to the user (generally called once all curves have been added.)frame
- The frame to display the graph in.public void printList(java.util.LinkedHashMap<java.lang.String,java.lang.Double> l)
l
- The list containing the Newton-Raphon calculated values.public java.util.LinkedHashMap<java.lang.String,java.lang.Double> newtonRaphson(double[][] data, double mu, double sigma, double m)
data
- The citation data in days.mu
- The initial mu guess to use in the Newton-Raphson method.sigma
- The initial sigma guess to use in the Newton-Raphson method.m
- The constant value, which is determined by the average number of references in each new paper for a journal.public static java.util.ArrayList<java.util.LinkedHashMap<java.lang.String,java.lang.Double>> newtonRaphson_ConvergenceTest(double[][] data, double step, double m)
data
- The citation data in days.step
- The step you would like to use to step through the interval of .1 to 10.m
- The average number of new references contained in each paper for a journal.public static void printMatrix(java.util.ArrayList<java.util.ArrayList<java.lang.Double>> l, java.lang.String[] header)
l
- Citation History.header
- Headers for columns.public double getLambda(double[][] data, double mu, double sigma, double m, double t, double n)
data
- The citation data in days.mu
- The solution for mu.sigma
- The solution for sigma.m
- The average number of references for new papers for a journal.t
- The last timestamp for the citation data.n
- The total number of citations from the citation history.public static java.lang.String toString(double[][] data)
data
- The citation history.


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