Stochastic Probing Research Articles

Analysis of stochastic probing methods for estimating the trace of functions of sparse symmetric matrices

We consider the problem of estimating the trace of a matrix function f ( A ) f(A) . In certain situations, in particular if f ( A ) f(A) cannot be well approximated by a low-rank matrix, combining probing methods based on graph colorings with stochastic trace estimation techniques can yield accurate approximations at moderate cost. So far, such methods have not been thoroughly analyzed, though, but were rather used as efficient heuristics by practitioners. In this manuscript, we perform a detailed analysis of stochastic probing methods and, in particular, expose conditions under which the expected approximation error in the stochastic probing method scales more favorably with the dimension of the matrix than the error in non-stochastic probing. Extending results from Aune, Simpson, and Eidsvik [Stat. Comput. 24 (2014), pp. 247–263], we also characterize situations in which using just one stochastic vector is always—not only in expectation—better than the deterministic probing method. Several numerical experiments illustrate our theory and compare with existing methods.

Improved Online Contention Resolution for Matchings and Applications to the Gig Economy

Motivated by applications in the gig economy, we study approximation algorithms for a sequential pricing problem. The input is a bipartite graph [Formula: see text] between individuals I and jobs J. The platform has a value of vj for matching job j to an individual worker. In order to find a matching, the platform can consider the edges [Formula: see text] in any order and make a one-time take-it-or-leave-it offer of a price [Formula: see text] of its choosing to i for completing j. The worker accepts the offer with a known probability pijw; in this case, the job and the worker are irrevocably matched. What is the best way to make offers to maximize revenue and/or social welfare? The optimal algorithm is known to be NP-hard to compute (even if there is only a single job). With this in mind, we design efficient approximations to the optimal policy via a new random-order online contention resolution scheme (RO-OCRS) for matching. Our main result is a 0.456-balanced RO-OCRS in bipartite graphs and a 0.45-balanced RO-OCRS in general graphs. These algorithms improve on the recent bound of [Formula: see text] and improve on the best-known lower bounds for the correlation gap of matching, despite applying to a significantly more restrictive setting. As a consequence of our online contention resolution scheme results, we obtain a 0.456-approximate algorithm for the sequential pricing problem. We further extend our results to settings where workers can only be contacted a limited number of times and show how to achieve improved results for this problem via improved algorithms for the well-studied stochastic probing problem. Funding: This work was supported by the National Science Foundation [Grant CCF2209520] and a gift from Amazon Research.

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor.

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

Fully Dynamic Online Selection through Online Contention Resolution Schemes

We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.

Stochastic probes in delay viral infection model with general incidence rate and control strategies

An analytical expedition to spotlight vital role of incidence rates in epidemic models is exemplified via delayed virus infection model perturbed with Gaussian white noise in this article. A stochastic model structure with time delay in general incidence rate accomplished our assertion on the role of infection transmission rates in the course of viral dynamics. Stability properties exhibited by model system around equilibrium solutions are rigorously analyzed using Lyapunov technique. We have also strengthened our theoretical achievements with empirical substantiations and visualized them as graphical representations. Our exemplifications showcased intricate relationship between model dynamics and incidence rates in unison.

Practical imaging algorithms in ultra-wideband radar systems using active aperture synthesis and stochastic probing signals

The subject of the manuscript is the algorithms for radar imaging. This research develops imaging methods and algorithms for wideband and ultrawideband active aperture synthesis systems with antenna arrays and stochastic probing signals. The use of antenna arrays makes it possible to obtain radar images without the need to move radar or antenna system in space. The use of wideband and ultra-wideband stochastic probing signals is justified by their narrow autocorrelation functions. This increased the resolution of the obtained images. The main idea of the proposed algorithms is to filter the original wideband signal into several narrowband processes. Furthermore, only the central frequencies of each narrowband signal were processed. This approach allows us to use the classical widespread methods of aperture synthesis for the case of a wideband signal. Usually, they are applicable only for narrowband signals that satisfy the condition of a quasi-monochromatic approximation. This significantly reduces the overall computational complexity of the imaging algorithm, which simplifies its further practical implementation on the existing radioelement base. Because of the simulation, a primary radar image has been obtained and the overall performance of the proposed approach to processing wideband signals has been confirmed. An increase in the quality of the obtained image when using a multiple of frequency ranges is shown. An experimental study of the effect of processing a wideband signal only at its centre frequency instead of the entire frequency band is conducted. During the experiment, the correlation functions of the signals received by two spaced receivers were obtained. As a result, the Van Cittert-Zernike theorem has been experimentally confirmed. It allows signal processing only at its centre frequency instead of the entire frequency band. Simultaneously, the prospect of expanding the bandwidth of the probing signal is indicated. It, in the presence of a wideband element base and devices for high-speed signal processing, will further increase the imaging resolution of a radar system.

Signal Processing Algorithm for Monopulse Noise Noncoherent Wideband Helicopter Altitude Radar

Radio altimeters are an important component of modern helicopter on-board systems. These devices currently involve the use of narrowband deterministic signals, that limits their potential technical characteristics. Given the significant breakthrough in the development of wideband and ultra-wideband radio electronics, it is promising to create on-board radio complexes capable of obtaining the necessary information using wideband stochastic signals. At the same time, when developing such complexes, it is important to use optimal synthesis methods for radio systems, which will allow optimal signal processing algorithms and potential accuracy parameters to be obtained. In this work, the algorithm to measure flight altitude for a helicopter or an unmanned aerial vehicle based on the processing of wideband and ultra-wideband pulsed stochastic signals is synthesized for the first time by the maximum-likelihood method. When formulating the problem, the mathematical model of the signal and observation is specified, and their statistical characteristics are investigated. The peculiarity of the synthesis task is the use of a noise pulse transmitter, which implements the function of an underlying surface illuminator, as well as considering the signal structure destruction during its radiation, propagation, and reflection. This signal shape destruction makes it impossible to synthesize a radar with internally coherent processing when working on one receiving antenna. In accordance with the synthesized algorithm, a simulation model of a pulsed radar with a stochastic probing signal has been developed and the results of its modeling are presented.

Алгоритм обробки сигналів для вертолітного широкосмугового шумового некогерентного радіовисотоміру

The algorithm for a helicopter or an unmanned aerial vehicle flight altitude measuring based on the processing of broadband and ultra-wideband pulsed stochastic signals has been synthesized for the first time by the maximum likelihood method. When formulating the initial data, mathematical models of the probing signal and the received observation are given, taking into account both various options for input path implementation, which impose restrictions on the observation equation form, and the geometry of the problem. When solving the problem, the statistical characteristics of the given models were found and studied. The calculated observation correlation function contains information about both the signal delay time and the radio pulse envelope, which makes it possible to obtain the algorithm for desired altitude parameter determining by one of two ways: differentiating the likelihood functional by the delay time or by the radio pulse envelope. At the same time, for the first time, the inversion equation for the statistical characteristics of the studied non-stationary processes in the frequency domain has been obtained. Such processes arise due to the presence of a radio pulse envelope. An important feature of the solved synthesis problem is a noise pulse transmitter use that implements the function of the underlying surface sounding, as well as taking into account the fact of the signal structure destruction during its radiation, propagation and reflection. Such a destruction of the signal shape doesn’t make it impossible to synthesize a radar with internal coherent processing algorithms when working on one receiving antenna and requires the search for other signal processing options. The use of a non-deterministic signal in the system also complicates the formalization of the delay time parameter in the likelihood function, since in this case the reference signal cannot be represented as a model or an analytical equation. Following the synthesized algorithm, a simulation model of a pulsed radar with a stochastic probing signal has developed and the results of its modeling are presented. The obtained output effect of the system fully corresponds to the classical theoretical calculations.

Transient measurement of phononic states with covariance-based stochastic spectroscopy

We present a novel approach to transient Raman spectroscopy, which combines stochastic probe pulses and a covariance-based detection to measure stimulated Raman signals in alpha-quartz. A coherent broadband pump is used to simultaneously impulsively excite a range of different phonon modes, and the phase, amplitude, and energy of each mode are independently recovered as a function of the pump–probe delay by a noisy-probe and covariance-based analysis. Our experimental results and the associated theoretical description demonstrate the feasibility of 2D-Raman experiments based on the stochastic-probe schemes, with new capabilities not available in equivalent mean-value-based 2D-Raman techniques. This work unlocks the gate for nonlinear spectroscopies to capitalize on the information hidden within the noise and overlooked by a mean-value analysis.

Online Contention Resolution Schemes with Applications to Bayesian Selection Problems

We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique, which we call online contention resolution schemes (OCRSs), is applicable to many online selection problems, including Bayesian online selection, oblivious posted pricing mechanisms, and stochastic probing models. It allows for handling a wide set of constraints and shares many strong properties of offline contention resolution schemes. In particular, OCRSs for different constraint families can be combined to obtain an OCRS for their intersection. Moreover, we can approximately maximize submodular functions in the online settings we consider. We thus get a broadly applicable framework for several online selection problems, which improves on previous approaches in terms of the types of constraints that can be handled, the objective functions that can be dealt with, and the assumptions on the strength of the adversary. Furthermore, we resolve two open problems from the literature; namely, we present the first constant-factor constrained oblivious posted price mechanism for matroid constraints and the first constant-factor algorithm for weighted stochastic probing with deadlines.

Time and frequency resolved transient-absorption and stimulated-Raman signals of stochastic light.

Covariance spectroscopy signals based on the transmission of broadband stochastic probe light undergoing a nonlinear optical process with matter are studied. The resulting signal depends on intensity correlation functions of the probe pulse. Application is made to transient absorption and stimulated Raman signals, where an ultraviolet pump and a delayed stochastically modulated infrared or optical Raman probe are used for monitoring vibrational excitations. We show that the stochastic properties of light can be exploited to circumvent the limitations on the joint temporal and spectral resolution of the signal. We study a model system with a time-dependent frequency and show that the dynamical information can be fully extracted from the covariance signal. This information is heavily suppressed upon averaging of noisy signals and practically inaccessible in conventional stimulated Raman measurements.

Identification of Protein Targets of Bioactive Small Molecules Using Randomly Photomodified Probes.

Identifying protein targets of bioactive small molecules often requires complex, lengthy development of affinity probes. We present a method for stochastic modification of small molecules of interest with a photoactivatable phenyldiazirine linker. The resulting isomeric mixture is conjugated to a hydrophilic copolymer decorated with biotin and a fluorophore. We validated this approach using known inhibitors of several medicinally relevant enzymes. At least a portion of the stochastic derivatives retained their binding to the target, enabling target visualization, isolation, and identification. Moreover, the mix of stochastic probes could be separated into fractions and tested for binding affinity. The structure of the active probe could be determined and the probe resynthesized to improve binding efficiency. Our approach can thus enable rapid target isolation, identification, and visualization, while providing information required for subsequent synthesis of an optimized probe.

Telomerase Activity Detection with Amplification-Free Single Molecule Stochastic Binding Assay.

Because the elongation of telomeres has been associated with tumorigenesis, it is of great interest to develop rapid and high-confidence telomerase activity detection methods for disease diagnosis. Currently, amplification-based strategies have been extensively explored for telomerase detection in vitro and in vivo. However, amplification is typically associated with poor reproducibility and high background, which hamper further applications of the strategies, particularly for real sample assays. Here, we demonstrate a new amplification-free single molecule imaging method for telomerase activity detection in vitro based on nucleic acid stochastic binding with total internal reflection fluorescence microscopy. The dynamic stochastic binding of a short fluorescent DNA probe with a genuine target yields a distinct kinetic signature from the background noise, allowing us to identify telomerase reaction products (TRPs) at the single molecule level. A limit-of-detection as low as 0.5 fM and a dynamic range of 0.5-500 fM for TRP detection were readily achieved. With this method, telomerase extracted from cancer cells was determined with sensitivity down to 10 cells. Moreover, the length distribution of TRPs was also determined by multiple stochastic probing, which could provide deep insight into the mechanistic study of telomerase catalysis.

Serotonin in Space: Understanding Single Fibers

All brain regions contain fibers that store and release 5-hydroxytryptamine (5-HT, serotonin). Since these fibers often do not have well-defined trajectories, most studies have focused on their overall densities, a measure that can be associated with local 5-HT tone in heathy and diseased brains. However, the observed fiber densities are the consequence of the behavior of single fibers. Evidence is presented as to why understanding single-fiber trajectories is important for basic and clinical neuroscience. In particular, serotonergic fibers can be viewed as natural, readily detectable stochastic probes that sample the invisible microarchitecture of brain tissue.

Submodular Stochastic Probing on Matroids

In a stochastic probing problem we are given a universe E, and a probability that each element e in E is active. We determine if an element is active by probing it, and whenever a probed element is active, we must permanently include it in our solution. Moreover, throughout the process we need to obey inner constraints on the set of elements taken into the solution, and outer constraints on the set of all probed elements. All previous algorithmic results in this framework have considered only the problem of maximizing a linear function of the active elements. Here, we consider submodular objectives.We provide new, constant-factor approximations for maximizing a monotone submodular function subject to multiple matroid constraints on both the elements that may be taken and the elements that may be probed. We also obtain an improved approximation for linear objective functions, and show how our approach may be generalized to handle k-matchoid constraints.

Resolution analysis by random probing

AbstractWe develop and apply methods for resolution analysis in tomography, based on stochastic probing of the Hessian or resolution operators. Key properties of our methods are (i) low algorithmic complexity and easy implementation, (ii) applicability to any tomographic technique, including full‐waveform inversion and linearized ray tomography, (iii) applicability in any spatial dimension and to inversions with a large number of model parameters, (iv) low computational costs that are mostly a fraction of those required for synthetic recovery tests, and (v) the ability to quantify both spatial resolution and interparameter trade‐offs. Using synthetic full‐waveform inversions as benchmarks, we demonstrate that autocorrelations of random‐model applications to the Hessian yield various resolution measures, including direction‐ and position‐dependent resolution lengths and the strength of interparameter mappings. We observe that the required number of random test models is around five in one, two, and three dimensions. This means that the proposed resolution analyses are not only more meaningful than recovery tests but also computationally less expensive. We demonstrate the applicability of our method in a 3‐D real‐data full‐waveform inversion for the western Mediterranean. In addition to tomographic problems, resolution analysis by random probing may be used in other inverse methods that constrain continuously distributed properties, including electromagnetic and potential‐field inversions, as well as recently emerging geodynamic data assimilation.

Application of stochastic probing radio signals for the range-velocity ambiguity resolution in doppler weather radars

Methods of expanding unambiguous measurement band of the range and radial velocity have been discussed on the basis of the uncertainty relation. The uncertainty function was derived, and properties of a sequence of stochastic radio pulses were analyzed. The use of the sequence of stochastic radio pulses for probing was shown to allow the problem of unambiguous measurement of the range and the estimation of the first three moments of Doppler spectrum of extended targets to be solved under conditions of the presence of “dead areas”.

On the intersection of independence systems

We study the properties of the intersection of independence systems. An independence system (V,I) is a k-system if for all S⊆V the ratio of the cardinality of the largest to the smallest maximal independent subset of S is at most k. We show that the intersection of a k1-system and a k2-system is a (k1+k2)-system.As an application of our results, we show an improved approximation algorithm for stochastic probing with deadlines over k-systems.

Performance Specification and Evaluation with Unified Stochastic Probes and Fluid Analysis

Rapid and accessible performance evaluation of complex software systems requires two critical features: the ability to specify useful performance metrics easily and the capability to analyze massively distributed architectures, without recourse to large compute clusters. We present the unified stochastic probe, a performance specification mechanism for process algebra models that combines many existing ideas: state and action-based activation, location-based specification, many-probe specification, and immediate signaling. These features, between them, allow the precise and compositional construction of complex performance measurements. The paper shows how a subset of the stochastic probe language can be used to specify common response-time measures in massive process algebra models. The second contribution of the paper is to show how these response-time measures can be analyzed using so-called fluid techniques to produce rapid results. In doing this, we extend the fluid approach to incorporate immediate activities and a new type of response-time measure. Finally, we calculate various response-time measurements on a complex distributed wireless network of O(10129) states in size.

Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs

We introduce a multi-input stochastic extremum seeking algorithm to solve the problem of seeking Nash equilibria for a noncooperative game whose N players seek to maximize their individual payoff functions. The payoff functions are general (not necessarily quadratic), and their forms are not known to the players. Our algorithm is a nonmodel-based approach for asymptotic attainment of the Nash equilibria. Different from classical game theory algorithms, where each player employs the knowledge of the functional form of his payoff and the knowledge of the other players' actions, a player employing our algorithm measures only his own payoff values, without knowing the functional form of his or other players' payoff functions. We prove local exponential (in probability) convergence of our algorithms. For nonquadratic payoffs, the convergence is not necessarily perfect but may be biased in proportion to the third derivatives of the payoff functions and the intensity of the stochastic perturbations used in the algorithm. We quantify the size of these residual biases. Compared to the deterministic extremum seeking with sinusoidal perturbation signals, where convergence occurs only if the players use distinct frequencies, in our algorithm each player simply employs an independent ergodic stochastic probing signal in his seeking strategy, which is realistic in noncooperative games. As a special case of an N-player noncooperative game, the problem of standard multivariable optimization (when the players' payoffs coincide) for quadratic maps is also solved using our stochastic extremum seeking algorithm.