As of March 2024, OpenAI o1 was the large language model (LLM) tool that had the best benchmark score in solving math problems, with a score of **** percent. Close behind, in second place, was OpenAI o1-mini, followed by GPT-4o.

Australian and New Zealand journal of statistics Impact Factor 2024-2025 - ResearchHelpDesk - The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems. In addition, suitable review papers and articles of historical and general interest will be considered. The journal also publishes book reviews on a regular basis. Abstracting and Indexing Information Academic Search (EBSCO Publishing) Academic Search Alumni Edition (EBSCO Publishing) Academic Search Elite (EBSCO Publishing) Academic Search Premier (EBSCO Publishing) CompuMath Citation Index (Clarivate Analytics) Current Index to Statistics (ASA/IMS) Journal Citation Reports/Science Edition (Clarivate Analytics) Mathematical Reviews/MathSciNet/Current Mathematical Publications (AMS) RePEc: Research Papers in Economics Science Citation Index Expanded (Clarivate Analytics) SCOPUS (Elsevier) Statistical Theory & Method Abstracts (Zentralblatt MATH) ZBMATH (Zentralblatt MATH)

Get Exam Question Paper Solutions of Mathematical Statistics and many more.

Suppose we observe a random vector X from some distribution in a known family with unknown parameters. We ask the following question: when is it possible to split X into two pieces f(X) and g(X) such that neither part is sufficient to reconstruct X by itself, but both together can recover X fully, and their joint distribution is tractable? One common solution to this problem when multiple samples of X are observed is data splitting, but Rasines and Young offers an alternative approach that uses additive Gaussian noise—this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this article, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on several prototypical applications, such as post-selection inference for trend filtering and other regression problems, and effect size estimation after interactive multiple testing. Supplementary materials for this article are available online.

Experiment 1: The main effect of distance, of RC Type, and their interaction on question-response accuracy; and the effect of distance within subject and object relatives.

These datatasets relate to the computational study presented in the paper The Berth Allocation Problem with Channel Restrictions, authored by Paul Corry and Christian Bierwirth. They consist of all the randomly generated problem instances along with the computational results presented in the paper.

Results across all problem instances assume ship separation parameters of [delta_1, delta_2, delta_3] = [0.25, 0, 0.5].

Excel Workbook Organisation:

The data is organised into separate Excel files for each table in the paper, as indicated by the file description. Within each file, each row of data presented (aggregating 10 replications) in the corrsponding table is captured in two worksheets, one with the problem instance data, and the other with generated solution data obtained from several solution methods (described in the paper). For example, row 3 of Tab. 2, will have data for 10 problem instances on worksheet T2R3, and corresponding solution data on T2R3X.

Problem Instance Data Format:

On each problem instance worksheet (e.g. T2R3), each row of data corresponds to a different problem instance, and there are 10 replications on each worksheet.

The first column provides a replication identifier which is referenced on the corresponding solution worksheet (e.g. T2R3X).

Following this, there are n*(2c+1) columns (n = number of ships, c = number of channel segmenets) with headers p(i)_(j).(k)., where i references the operation (channel transit/berth visit) id, j references the ship id, and k references the index of the operation within the ship. All indexing starts at 0. These columns define the transit or dwell times on each segment. A value of -1 indicates a segment on which a berth allocation must be applied, and hence the dwell time is unkown.

There are then a further n columns with headers r(j), defining the release times of each ship.

For ChSP problems, there are a final n colums with headers b(j), defining the berth to be visited by each ship. ChSP problems with fixed berth sequencing enforced have an additional n columns with headers toa(j), indicating the order in which ship j sits within its berth sequence. For BAP-CR problems, these columnns are not present, but replaced by n*m columns (m = number of berths) with headers p(j).(b) defining the berth processing time of ship j if allocated to berth b.

Solution Data Format:

Each row of data corresponds to a different solution.

Column A references the replication identifier (from the corresponding instance worksheet) that the soluion refers to.

Column B defines the algorithm that was used to generate the solution.

Column C shows the objective function value (total waiting and excess handling time) obtained.

Column D shows the CPU time consumed in generating the solution, rounded to the nearest second.

Column E shows the optimality gap as a proportion. A value of -1 or an empty value indicates that optimality gap is unknown.

From column F onwards, there are are n*(2c+1) columns with the previously described p(i)_(j).(k). headers. The values in these columns define the entry times at each segment.

For BAP-CR problems only, following this there are a further 2n columns. For each ship j, there will be columns titled b(j) and p.b(j) defining the berth that was allocated to ship j, and the processing time on that berth respectively.

Australian and New Zealand journal of statistics - ResearchHelpDesk - The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association. The main body of the journal is divided into three sections. The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data. The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context. The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems. In addition, suitable review papers and articles of historical and general interest will be considered. The journal also publishes book reviews on a regular basis. Abstracting and Indexing Information Academic Search (EBSCO Publishing) Academic Search Alumni Edition (EBSCO Publishing) Academic Search Elite (EBSCO Publishing) Academic Search Premier (EBSCO Publishing) CompuMath Citation Index (Clarivate Analytics) Current Index to Statistics (ASA/IMS) Journal Citation Reports/Science Edition (Clarivate Analytics) Mathematical Reviews/MathSciNet/Current Mathematical Publications (AMS) RePEc: Research Papers in Economics Science Citation Index Expanded (Clarivate Analytics) SCOPUS (Elsevier) Statistical Theory & Method Abstracts (Zentralblatt MATH) ZBMATH (Zentralblatt MATH)

Google Gemini Statistics: In 2023, Google unveiled the most powerful AI model to date. Google Gemini is the world’s most advanced AI leaving the ChatGPT 4 behind in the line. Google has 3 different sizes of models, superior to each, and can perform tasks accordingly. According to Google Gemini Statistics, these can understand and solve complex problems related to absolutely anything. Google even said, they will develop AI in such as way that it will let you know how helpful AI is in our daily routine. Well, we hope our next generation won’t be fully dependent on such technologies, otherwise, we will lose all of our natural talent! Editor’s Choice Google Gemini can follow natural and engaging conversations. According to Google Gemini Statistics, Gemini Ultra has a 90.0% score on the MMLU benchmark for testing the knowledge of and problem-solving on subjects including history, physics, math, law, ethics, history, and medicine. If you ask Gemini what to do with your raw material, it can provide you with ideas in the form of text or images according to the given input. Gemini has outperformed ChatGPT -4 tests in the majority of the cases. According to the report this LLM is said to be unique because it can process multiple types of data at the same time along with video, images, computer code, and text. Google is considering its development as The Gemini Era, showing the importance of our AI is significant in improving our daily lives. Google Gemini can talk like a real person Gemini Ultra is the largest model and can solve extremely complex problems. Gemini models are trained on multilingual and multimodal datasets. Gemini’s Ultra performance on the MMMU benchmark has also outperformed the GPT-4V in the following results Art and Design (74.2), Business (62.7), Health and Medicine (71.3), Humanities and Social Science (78.3), and Technology and Engineering (53.00).

This dataset contains research output from studying the Transit Network Design Problem (TNDP). At a high level, the dataset includes: a novel transit network based on the Brisbane transport infrastructure, and results from the testing of new methods on the Brisbane network and existing benchmark networks (Mandl and Mumford).

This dataset contains four subsets of data, and are related to Joshua Rosentreter's PhD Thesis. These are outlined below:

Transit Network Dataset: A novel transit network for researchers to use when addressing the Transit Network Planning Problem. The network is based on the Brisbane City transportation infrastructure.
MIP Model for TNFSP: Evaluations of existing solutions to the TNDP and TNDFSP using a variety of existing methods and a proposed mixed integer programming (MIP) model.
Meta-Heuristic Method for TNDFSP: Results from a novel (adapted from existing) method designed to target the hub-and- spoke style structure of the demand within a metropolitan city based network.
Hybrid Method for TNDFSP: Results from a novel method created through the hybridisation of the MIP model and meta-heuristic method.

Further descriptions of the data are contained in the subfolders within.

This is a data repository for the paper "Binary classification as a phase separation process", by Rafael Monteiro.

• Website with description of this project: https://rafael-a-monteiro-math.github.io/Binary_classification_phase_separation/index.html
• Github: https://github.com/rafael-a-monteiro-math/Binary_classification_phase_separation

They contain

• Examples
• 1D toy model examples
• Computational statistics
• Several trained PSBC on MNIST dataset, with different parameter configurations
• Extra simulations, investigating normalization properties, low dimensional models that fail due to "too much" model compression, and comparison among ANNs, KNNs, and the PSBC in 1D

If you want to know

1. how to read the data
2. how to access computational statistics, raw data, and examples
3. how to use the data stored in this data repository

see the guide README.pdf on GitHub page at Binary_Classification_Phase_Separation, where a script that downloads (and organizes) all this data is also available ("download_PSBC.sh).

I did not include a copy of the train-test set (0-1dubset of the MNIST database) in every folder with simulations. But you can find a copy of the normalized dataset in the tar ball "PSBC_Examples.tar.gz" as

data_test_normalized_MNIST.csv and data_train_normalized_MNIST.csv.

Question Paper Solutions of chapter Applied Statistics of Mathematics - II A, 2nd Semester , Computer Science and Engineering

Mathematics is strongly connected to gambling through the mathematical models underlying any game of chance. Mathematics is reflected not only in games’ design/characteristics and their outcomes, but also in gamblers’ perception and knowledge of the mathematics-related facts of gambling – which influence their gambling behavior. The math-indispensability principle (Bărboianu, 2013) applies not only in problem-gambling research, but also in the gambling industry. The structural, informative, strategic, psychological, pathological, and ethical aspects of gambling have been identified to be grounded in the mathematics of games and gambling (Griffiths, 1993; Bărboianu 2014, 2015; Turner & Hobay, 2004; Harrigan, 2009, and others).In this theoretical framework, research is able to derive concrete norms and criteria to adequately reflect the mathematical dimension of gambling in the communication and texts associated with the gambling industry. These norms and criteria of adequacy will be further communicated to policy and decision makers in both governmental and private sectors, with the recommendation for implementation. Our study aims to evaluate qualitatively the reflection of the mathematical dimension of gambling in the content of gambling websites. This analysis is necessary in order to have an objective and concrete image of the actual state of this matter in the online industry and of the challenges that such research and application would face in the real world of gambling. A minimum number of 600 gambling websites will be reviewed annually for their content in that respect. A statistical analysis will record the presence of the mathematical dimension of gambling and its forms in the content of participating websites, and a qualitative research will analyze and assess the quality of the content with respect to that dimension.

Question Paper Solutions of chapter Applied Statistics of Mathematics III, 3rd Semester , Mechanical Engineering

Bayesian reasoning - the optimal process of updating a hypothesis or belief with new information - is a critical aspect of both everyday decision-making and statistics education, but strategies for effectively teaching the topic in the classroom remain elusive. This study leverages the findings of prior research on facilitating Bayesian reasoning by utilizing a visualization, called the bar display, as a method for teaching Bayes theorem and its underlying probability concepts. Data were collected from a college-level statistics-in-psychology course, wherein students were taught and tested on Bayesian reasoning either with or without the bar display. In addition to testing the immediate efficacy of the bar display, data were also collected to test long-term retention and the potential differential benefits for low numeracy and high anxiety students. Results indicated engagement with the bar display as a method for visually approximating answers to Bayesian questions, with students trained with the bar display providing more accurate answers to Bayesian reasoning questions before training and at long-term assessment. Additionally, students with self-reported low numeracy and high math anxiety performed better on Bayesian reasoning questions when learning with the bar display. Recommendations for future implementations are discussed.

website | paper

  AceMath RM Training Data Card

We release the AceMath RM Training data that is used to train the AceMath-7/72B-RM for math outcome reward modeling. Below is the data statistics:

number of unique math questions: 356,058 number of examples: 2,136,348 (each questions have 6 different responses)

  Benchmark Results (AceMath-Instruct + AceMath-72B-RM)

We compare AceMath to leading proprietary and open-access math models in above Table. Our… See the full description on the dataset page: https://huggingface.co/datasets/nvidia/AceMath-RM-Training-Data.

All population characteristics in the table were identical for the synthetic microdata and the American Community Survey data.

Topic: generating uniform random samples from the set of all integer partitions for a given total N and a number of parts S.Problem: current random integer partitioning functions of mathematical software can take a long time to generate a single partition for a given N (regardless of S) and an untennable amount of time generating partitions of N with S parts. Currently, no function among math softwares, peer-reviewed literature, and on stackexchange and arxiv.org generates random partitions with respect to both N and S. Consequently, if one is interested in generating random integer partitions for N having S parts, then one must usually waste time generating random partitions of N and rejecting those not matching S. Note! I have since solved this problem definitively: The question is asked and the solution is presented here: stackoverflow.com/questions/10287021/an-algorithm-for-randomly-generating-integer-partitions-of-a-particular-length/12742508#12742508 I've recently published a preprint of a manuscript on figshare outlining a simple and unbiased solution to this question. figshare.com/articles/Random_integer_partitions_with_restricted_numbers_of_parts/156290 However, below is an approach I tried and was unable to eliminate sampling bias from while keeping reasonable speed. I guess this page is more useful as a good way to NOT go about getting random integer partitions for N and S. Deprecated alternative approach (often biased and slower than the above solution): Generate a single random partition of N and randomly manipulate it until its number of parts equals S. Why? Because randomly perturbing a partition of N until it satisfies S can be faster than generating random partitions based solely on N and rejecting those without S parts.Contents (results of deprecated algorithm): Visual comparisons of 500 random samples generated from the new function derived by myself (red curves) against 500 random samples generated using the random partition function found in the Sage mathematical environment (black curves). Kernel density curves (red ones and black ones) are for statistical evenness across the partition. Statistical evenness is a standardized log-transform of the variance. Kernel density cures that overlap nearly completely reveal that the random samples of partitions generated between the two approaches share a similar structure. Evenness is estimated using Evar, a transform of the variance of log summand values. Evar is standardized to take values between 0.0 (no evenness) and 1.0 (perfect evenness). Close agreement between the random manipulation approach and the Sage function (very high rejection rates as most partitions of N don't match S) was also found using other statistical characteristics (e.g. median summand, relative size of largest summand). These results reveal that the statistical quality of evenness (a transform of the variance) is in high agreement between the two approaches (Sage's function and the potential alternative of randomly manipulating integer partitions using conjugates).Note: I have found biases in skewness and the median summand value with this type of method (randomly manipulate an integer partition to arrive at a uniform random sample based on N and S), and would not recommend this approach.

LogicJa Dataset Card

  Overview

LogicJa is a multi-turn benchmark designed to assess the reasoning capabilities of Japanese language models across multiple domains. This dataset consists of 105 multi-turn tasks (each containing two questions) for a total of 210 questions. Each category has 30 questions to ensure statistical significance.

Category Reasoning Math Writing Coding Understanding Grammar Culture Total

Multi-turn Tasks 15 15 15 15 15 15 15 105… See the full description on the dataset page: https://huggingface.co/datasets/sionic-ai/LogicJa.

Number of positive and negative examples for each functional site.

Rubric Questions.