Probabilistic Computation Research Articles

Statistical Verification of PCTL Using Stratified Samples

In this work, we propose a stratified sampling method to statistically check Probabilistic Computation Tree Logic (PCTL) formulas on discrete-time Markov chains with sequential probability ratio test. Distinct from previous statistical verification methods using independent Monte Carlo sampling, our algorithm uses stratified samples that are negatively correlated, thus give lower variance. The experiments demonstrate that the new algorithm uses a smaller number of samples for a given confidence level on several benchmark examples.

Estimating efficiency in a spatial autoregressive stochastic frontier model

The spatial autoregressive stochastic frontier model of Glass et al.(2016) is based on distributional assumptions on two-sided and one-sided error terms. After estimating the model parameters, the efficiency estimates need to be corrected due to the presence of spatial autoregressive term in their model. Glass et al.(2016) estimate the corrected efficiencies by employing ideas from a distribution-free method on the efficiency estimation, which may be sensitive to outliers. We propose an alternative way to correct efficiency estimates that is in line with the distribution-based methods.

Superparamagnetic perpendicular magnetic tunnel junctions for true random number generators

Superparamagnetic perpendicular magnetic tunnel junctions are fabricated and analyzed for use in random number generators. Time-resolved resistance measurements are used as streams of bits in statistical tests for randomness. Voltage control of the thermal stability enables tuning the average speed of random bit generation up to 70 kHz in a 60 nm diameter device. In its most efficient operating mode, the device generates random bits at an energy cost of 600 fJ/bit. A narrow range of magnetic field tunes the probability of a given state from 0 to 1, offering a means of probabilistic computing.

An Enhanced Probabilistic Computation Method for the Weight Distribution of Polar Codes

Owning to the explicit structure, Hamming weight distribution (HWD) of polar codes with large length can be recursively computed with that of the short one. In this letter, an enhanced probabilistic computation method is proposed to estimate the HWD of polar codes. Only the uniform distribution assumption for the 1 s in the codeword is used and the exhaustively searched HWD for very short polar code are combined to improve the accuracy of the proposed method. Meanwhile, some characteristics for the HWD of polar codes are discussed and used to avoid the unnecessary calculations. Simulation results show that the estimated HWD matches the exact one well for rate larger than 0.5. With the obtained HWD, the asymptotic performance of polar codes can be accurately estimated in almost the whole rate range.

Prediction of reliability analysis of composite tubular structure under hygro-thermo-mechanical loading

ABSTRACTThe present paper focuses on reliability prediction of composite structure under hygro-thermo-mechanical loading, conditioned by Tsai-Wu failure criterion, where the Monte–Carlo method is used to estimate the failure probability(Pf). This model was developed in two steps: first, the development of a deterministic model, based on an analytical and numerical approach, and then, a probabilistic computation. Using the hoop stress for each ply, a sensitivity analysis was performed for random design variables, such as materials properties, geometry, manufacturing, and loading, on composite cylindrical structure reliability. The probabilistic results show the very high increase of failure probability when all parameters are considered.

Parametric Markov Chains: PCTL Complexity and Fraction-free Gaussian Elimination

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for the parameters. Among the tasks typically addressed in the analysis of parametric Markov chains are (1) the computation of closed-form solutions for reachabilty probabilities and other quantitative measures and (2) finding symbolic representations of the set of parameter valuations for which a given temporal logical formula holds as well as (3) the decision variant of (2) that asks whether there exists a parameter valuation where a temporal logical formula holds. Our contribution to (1) is to show that existing implementations for computing rational functions for reachability probabilities or expected costs in parametric Markov chains can be improved by using fraction-free Gaussian elimination, a long-known technique for linear equation systems with parametric coefficients. Our contribution to (2) and (3) is a complexity-theoretic discussion of the model checking problem for parametric Markov chains and probabilistic computation tree logic (PCTL) formulas. We present an exponential-time algorithm for (2) and a PSPACE upper bound for (3). Moreover, we identify fragments of PCTL and subclasses of parametric Markov chains where (1) and (3) are solvable in polynomial time and establish NP-hardness for other PCTL fragments.

Magic coins are useful for small-space quantum machines

Although polynomial-time probabilistic Turing machines can utilize uncomputable transition probabilities to recognize uncountably many languages with bounded error when allowed to use double logarithmic space, it is known that such “magic coins” give no additional computational power to constant-space versions of those machines. We show that adding a few quantum bits to the model changes the picture dramatically. For every language L, there exists such a two-way quantum finite automaton (2qcfa) that recognizes a language of the same Turing degree as L with bounded error in polynomial time. When used as verifiers in public-coin interactive proof systems, such automata can verify membership in all languages with bounded error, outperforming their classical counterparts, which are known to fail for the palindromes language. Corollaries demonstrate even faster machines when one is allowed to use a counter as memory, and an alternative proof of the uncountability of stochastic languages.

Efficient classical simulation of the Deutsch\u2013Jozsa and Simon\u2019s algorithms

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch–Jozsa and Simon’s problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch–Jozsa problem with probability 1 using only one oracle query, and Simon’s problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch–Jozsa and Simon’s problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.

Formal analysis and evaluation of the back-off procedure in IEEE802.11P VANET

The back-off procedure is one of the media access control technologies in 802.11P communication protocol. It plays an important role in avoiding message collisions and allocating channel resources. Formal methods are effective approaches for studying the performances of communication systems. In this paper, we establish a discrete time model for the back-off procedure. We use Markov Decision Processes (MDPs) to model the non-deterministic and probabilistic behaviors of the procedure, and use the probabilistic computation tree logic (PCTL) language to express different properties, which ensure that the discrete time model performs their basic functionality. Based on the model and PCTL specifications, we study the effect of contention window length on the number of senders in the neighborhood of given receivers, and that on the station’s expected cost required by the back-off procedure to successfully send packets. The variation of the window length may increase or decrease the maximum probability of correct transmissions within a time contention unit. We propose to use PRISM model checker to describe our proposed back-off procedure for IEEE802.11P protocol in vehicle network, and define different probability properties formulas to automatically verify the model and derive numerical results. The obtained results are helpful for justifying the values of the time contention unit.

Probabilistic Computations for Attention, Eye Movements, and Search.

The term visual attention immediately evokes the idea of limited resources, serial processing, or a zoom metaphor. But evidence has slowly accumulated that computations that take into account probabilistic relationships among visual forms and the target contribute to optimizing decisions in biological and artificial organisms, even without considering these limited-capacity processes in covert attention or even foveation. The benefits from such computations can be formalized within the framework of an ideal Bayesian observer and can be related to the classic theory of sensory cue combination in vision science and context-driven approaches to object detection in computer vision. The framework can account for a large range of behavioral findings across distinct experimental paradigms, including visual search, cueing, and scene context. I argue that these forms of probabilistic computations might be fundamental to optimizing decisions in many species and review human experiments trying to identify scene properties that serve as cues to guide eye movements and facilitate search. I conclude by discussing contributions of attention beyond probabilistic computations but argue that the framework's merit is to unify many basic paradigms to study attention under a single theory.

Revisiting Fuzzy Set and Fuzzy Arithmetic Operators and Constructing New Operators in the Land of Probabilistic Linguistic Computing

In this paper, we use a framework known as probabilistic linguistic computing (PLC) to achieve two goals. First, we demonstrate it as an easy-to-use laboratory for understanding existing fuzzy operators. This is achieved by projecting a fuzzy operator of interest into the PLC setting, arriving at a corresponding PLC operator, and hence revealing assumptions initially hidden in that operator. Second, we demonstrate PLC as a simple and general approach for the engineers to construct a wide range of fuzzy operators and measures that can be robustly used in their specialized applications. In particular, by explicating the assumptions hidden in the commonly used fuzzy set and fuzzy arithmetic operators, one is in position to develop other potentially more complex operators (such as fuzzy entropy measure or fuzzy partial correlation measures) that possess the same assumptions—these complex operators so developed can then be viewed as compatible and consistent with the commonly used fuzzy set and arithmetic operators.

Pcarrier: Individual and family distributions of a susceptibility gene for breast and ovarian cancer based on family history.

e13005 Background: Most of the BRCA1/2 and PALB2 analyses performed in patients with a personal and familial history (FH) of breast/ovarian cancer are negative. In this context, there is no targeted analysis available to identify relatives at high risk (carrier of the causal hypothetical mutated gene). Thus, the recommendations of surveillance to all relatives are based only on the FH of cancer. At the Institut Curie we assess the degree of severity of the FH by calculating the probability of carrying a single autosomal dominant susceptibility gene without taking into account genotyping results but using the LINKAGE software with the parameters of the Claus-Easton model (1993). This reliable but old tool has a slow console interactive interface (roughly 15 min of clinicians time for each assessed family). Methods: We rewrite the model as a Bayesian network combining Mendelian genetics with classical survival analysis. All probabilistic computations are performed through belief propagation (sum-product algorithm) over real numbers or polynomials. The programming language is C++. Results: pCarrier is a modern and efficient implementation of the Claus-Easton model for clinicians with the following features: 1) fast non-interactive command line ( < 1s to process a previously registered family) combined with a graphical user-friendly interface; 2) computations dealing with monozygotic twins or loops without any human intervention (ex: loop breaking); 3) choice between the original discretized model (individual FH into 14 classes) and its continuous version (piecewise constant hazard); 4) marginal individual carrier distribution for all individuals in the pedigree; 5) joint distribution of the number of carriers among any group of individuals (ex: in the entire family, among the living only). Conclusions: pCarrier is experimented since January 2017 in the Institut Curie as a replacement of the existing tool and appears so far to be dramatically faster and easier to use for the clinicians, highly reliable (consistence with the existing tool), and able to provide new useful decision-making probabilities using the distribution of the number of carriers.

Efficient estimation of functionals in nonparametric boundary models

For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes, we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation method which nevertheless depends on a Holder condition or monotonicity assumption for the underlying regression or boundary function. We first construct a simple blockwise estimator and then build up a nonparametric maximum-likelihood approach for exponential noise variables and the point process model. In that approach also non-asymptotic efficiency is obtained (UMVU: uniformly minimum variance among all unbiased estimators). The proofs rely essentially on martingale stopping arguments for counting processes and the point process geometry. The estimators are easily computable and a small simulation study confirms their applicability.

Fitting Endogenous Stochastic Frontier Models in Stata

In this article, I introduce sfkk, a new command for fitting endogenous stochastic frontier models. sfkk provides estimators for the parameters of a linear model with a disturbance assumed to be a mixture of two components: a measure of inefficiency that is strictly nonnegative and a two-sided error term from a symmetric distribution. sfkk can handle endogenous variables in the frontier or the inefficiency, and the sfkk estimates outperform the standard frontier estimates that ignore endogeneity.

Creating Affective Autonomous Characters Using Planning in Partially Observable Stochastic Domains

The ability to reason about and respond to their own emotional states can enhance the believability of Non-Player Characters (NPCs). In this paper, we use a Partially Observable Markov Decision Process (POMDP)-based framework to model emotion over time. A two-level appraisal model, involving quick and reactive vs. slow and deliberate appraisals, is proposed for the creation of affective autonomous characters based on POMDPs, wherein the probability of goal satisfaction is used in an appraisal and reappraisal process for emotion generation. We not only extend Probabilistic Computation Tree Logic (PCTL) for reasoning about the properties of emotional states based on POMDPs but also illustrate how four reactive (primary) emotions and nine deliberate (secondary) emotions can be derived by combining PCTL with the belief-desire theory of emotion. The results of an empirical study suggest that the proposed model can be used to create characters that appear to be more believable and more intelligent.

SFREEMAP - A simulation-free tool for stochastic mapping

BackgroundStochastic mapping is frequently used in comparative biology to simulate character evolution, enabling the probabilistic computation of statistics such as number of state transitions along a tree and distribution of states in its internal nodes. Common implementations rely on Continuous-time Markov Chain simulations whose parameters are difficult to adjust and subjected to inherent inaccuracy. Thus, researchers must run a large number of simulations in order to obtain adequate estimates. Although execution time tends to be relatively small when simulations are performed on a single tree assumed to be the “true” topology, it may become an issue if analyses are conducted on several trees, such as the ones that make up posterior distributions obtained via Bayesian phylogenetic inference. Working with such distributions is preferable to working with a single tree, for they allow the integration of phylogenetic uncertainty into parameter estimation. In such cases, detailed character mapping becomes less important than parameter integration across topologies. Here, we present an R-based implementation (SFREEMAP) of an analytical approach to obtain accurate, per-branch expectations of numbers of state transitions and dwelling times. We also introduce an intuitive way of visualizing the results by integrating over the posterior distribution and summarizing the parameters onto a target reference topology (such as a consensus or MAP tree) provided by the user.ResultsWe benchmarked SFREEMAP’s performance against make.simmap, a popular R-based implementation of stochastic mapping. SFREEMAP confirmed theoretical expectations outperforming make.simmap in every experiment and reducing computation time of relatively modest datasets from hours to minutes. We have also demonstrated that SFREEMAP returns estimates which were not only similar to the ones obtained by averaging across make.simmap mappings, but also more accurate, according to simulated data. We illustrate our visualization strategy using previously published data on the evolution of coloniality in scleractinian corals.ConclusionSFREEMAP is an accurate and fast alternative to ancestral state reconstruction via simulation-based stochastic mapping.

Abstract P3-13-11: Utility of LigaSureTM vessel-sealing device in axillary dissection for breast cancer surgery: A randomized single center study

Abstract Introduction Axillary lymph node dissection is standard therapy for patients with positive-node breast cancer, and can be performed with an electrocautery scalpel and suture ligation in most cases. However, knot slipping can occur during suture ligation and this can spread thermal damage to peripheral tissues. The LigaSureTM Small Jaw vessel-sealing system was developed as an alternative to suture ligatures, staplers, and other energy-dependent devices for sealing blood and lymphatic vessels, but its use in axillary dissection for breast cancer is limited. We prospectively compared the duration until drain removal after surgery, total lymph fluid drainage volume, intraoperative blood loss, and incidence of complications after axillary dissections, between this device and conventional methods. Methods This prospective randomized study was conducted at the Department of Breast and Endocrine Surgery at Tokai University School of Medicine, Kanagawa, Japan, between October 2011 and March 2015. Major eligibility criteria included (1) pathologically confirmed breast cancer diagnosis, (2) age ≥20 and ≤80 years, and (3) a signed informed consent form. The primary endpoint was duration until drain removal after surgery. The secondary endpoints were total lymph fluid drainage volume, intraoperative blood loss, and incidence of postoperative surgical complications. We defined the criterion for drain removal as a lymph fluid drainage volume of <40 mL/day for two consecutive days.The target accrual was 100 patients, with a two-sided error rate of 5%, and 90% power. The assumed duration until drain removal after surgery was 7.2 days in the control group (conventional use of an electrocautery scalpel and suture ligation) and 5.8 days in the study group (use of the LigaSureTM Small Jaw). This clinical study was approved by the Institutional Review Board of the Tokai University School of Medicine and is registered with UMIN (No. 000013034). Results Initially, 100 patients were assigned as eligible; however, two patients were later excluded because of the exclusion criteria. Of 98 patients, 49 were randomized to the study group, and 49 to the control group. The mean duration until drain removal after surgery was 5.2 days in the study group and 5.0 days in the control group (p=0.573). The mean total lymph fluid drainage volumes were 260.3 and 233.5 mL (p=0.502), and the mean intraoperative blood loss volumes were 17.8 and 18.0 mL (p=0.949), for the study and control groups, respectively. No significant differences were found between the two groups regarding drain removal duration, total drainage volume, and intraoperative blood loss volume. Both groups had low incidence rates of postoperative hematoma, wound infection, lymphedema, and pain, and had similar incidence rates of seroma formation after drain removal. Conclusion Our study results indicated that the use of the LigaSureTM Small Jaw in axillary dissection for breast cancer was as safe as conventional methods. However, using the LigaSureTM Small Jaw did not improve surgical outcomes such as duration until drain removal and total lymph fluid drainage volume compared with conventional methods. Citation Format: Okamura T, Niikura N, Yokoyama K, Ogiya R, Oshitanai R, Terao M, Morioka T, Tsuda B, Saito Y, Suzuki Y, Tokuda Y. Utility of LigaSureTM vessel-sealing device in axillary dissection for breast cancer surgery: A randomized single center study [abstract]. In: Proceedings of the 2016 San Antonio Breast Cancer Symposium; 2016 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2017;77(4 Suppl):Abstract nr P3-13-11.

An Alternative Specification for Technical Efficiency Effects in a Stochastic Frontier Production Function

This paper proposes an alternative specification for technical efficiency effects in a stochastic production frontier model. The proposed specification is distribution free and thus eschews one-sided error term present in almost all the existing inefficiency effects models. The efficiency effects are represented by the standard normal cumulative distribution function of exogenous variables which ensures the efficiency scores to lie in a unit interval. An empirical exercise based on widely used Philippines rice farming data set illustrates the simplicity and usefulness of the proposed model.

Fast iterative solution of the Bethe–Salpeter eigenvalue problem using low-rank and QTT tensor approximation

In this paper, we propose and study two approaches to approximate the solution of the Bethe–Salpeter equation (BSE) by using structured iterative eigenvalue solvers. Both approaches are based on the reduced basis method and low-rank factorizations of the generating matrices. We also propose to represent the static screen interaction part in the BSE matrix by a small active sub-block, with a size balancing the storage for rank-structured representations of other matrix blocks. We demonstrate by various numerical tests that the combination of the diagonal plus low-rank plus reduced-block approximation exhibits higher precision with low numerical cost, providing as well a distinct two-sided error estimate for the smallest eigenvalues of the Bethe–Salpeter operator. The complexity is reduced to O(Nb2) in the size of the atomic orbitals basis set, Nb, instead of the practically intractable O(Nb6) scaling for the direct diagonalization. In the second approach, we apply the quantized-TT (QTT) tensor representation to both, the long eigenvectors and the column vectors in the rank-structured BSE matrix blocks, and combine this with the ALS-type iteration in block QTT format. The QTT-rank of the matrix entities possesses almost the same magnitude as the number of occupied orbitals in the molecular systems, No<Nb, hence the overall asymptotic complexity for solving the BSE problem by the QTT approximation is estimated by O(log⁡(No)No2). We confirm numerically a considerable decrease in computational time for the presented iterative approaches applied to various compact and chain-type molecules, while supporting sufficient accuracy.

Cubic spline interpolation of functions with high gradients in boundary layers

The cubic spline interpolation of grid functions with high-gradient regions is considered. Uniform meshes are proved to be inefficient for this purpose. In the case of widely applied piecewise uniform Shishkin meshes, asymptotically sharp two-sided error estimates are obtained in the class of functions with an exponential boundary layer. It is proved that the error estimates of traditional spline interpolation are not uniform with respect to a small parameter, and the error can increase indefinitely as the small parameter tends to zero, while the number of nodes N is fixed. A modified cubic interpolation spline is proposed, for which O((ln N/N)4) error estimates that are uniform with respect to the small parameter are obtained.