Generic Reduction Research Articles

Obtaining Lower Query Complexities Through Lightweight Zeroth-Order Proximal Gradient Algorithms.

Zeroth-order (ZO) optimization is one key technique for machine learning problems where gradient calculation is expensive or impossible. Several variance, reduced ZO proximal algorithms have been proposed to speed up ZO optimization for nonsmooth problems, and all of them opted for the coordinated ZO estimator against the random ZO estimator when approximating the true gradient, since the former is more accurate. While the random ZO estimator introduces a larger error and makes convergence analysis more challenging compared to coordinated ZO estimator, it requires only O(1) computation, which is significantly less than O(d) computation of the coordinated ZO estimator, with d being dimension of the problem space. To take advantage of the computationally efficient nature of the random ZO estimator, we first propose a ZO objective decrease (ZOOD) property that can incorporate two different types of errors in the upper bound of convergence rate. Next, we propose two generic reduction frameworks for ZO optimization, which can automatically derive the convergence results for convex and nonconvex problems, respectively, as long as the convergence rate for the inner solver satisfies the ZOOD property. With the application of two reduction frameworks on our proposed ZOR-ProxSVRG and ZOR-ProxSAGA, two variance-reduced ZO proximal algorithms with fully random ZO estimators, we improve the state-of-the-art function query complexities from Omindn1/2ε2,dε3 to O˜n+dε2 under d>n12 for nonconvex problems, and from Odε2 to O˜nlog1ε+dε for convex problems. Finally, we conduct experiments to verify the superiority of our proposed methods.

Modelling and Prediction of Fe/MWCNT Nanocomposites for Hexavalent Chromium Reduction

Chromium (Cr) is a heavy metal pollutant prevalent in freshwater resources. Current investigations into Cr(VI) removal materials primarily involve multi-component materials. Among them, iron nanoparticles and multi-walled carbon nanotubes (MWCNTs) have exhibited great promise of removal capabilities. However, determining the optimal component ratio(s) experimentally still requires a substantial amount of effort. This paper presents a novel, model-based approach which can lessen the burden by predicting the performance of new materials. The model is based on reaction kinetics equations and derives its input parameters from the size and surface area characterisations of the components, individual components removal performance, and their mixture performance at one specific component ratio. The model is validated against experimental results for Fe/MWCNT mixtures at six ratios. The root mean square error of our model is 3.95 mg/g, which is less than 3% of the total adsorption capacity, indicating that the model is reliable. The model can be used to identify the optimal component ratios of the Fe-MWCNT composite and to reveal the relationship between performance and time. To the best of our knowledge, this is the first semi-empirical model that can predict the adsorption capacity of a composite material for heavy metals. The model is founded on the generic reduction theory of adsorption, and model parameters are not tied specifically to Fe/MWCNT. Thus, it can be used for predicting the adsorption reduction properties of other multiphase materials to speed up the new material design process.

Pushing the Limit of 1-Minimality of Language-Agnostic Program Reduction

Program reduction has demonstrated its usefulness in facilitating debugging language implementations in practice, by minimizing bug-triggering programs. There are two categories of program reducers: language-agnostic program reducers (AGRs) and language-specific program reducers (SPRs). AGRs, such as HDD and Perses, are generally applicable to various languages; SPRs are specifically designed for one language with meticulous thoughts and significant engineering efforts, e.g., C-Reduce for reducing C/C++ programs. Program reduction is an NP-complete problem: finding the globally minimal program is usually infeasible. Thus all existing program reducers resort to producing 1-minimal results, a special type of local minima. However, 1-minimality can still be large and contain excessive bug-irrelevant program elements. This is especially the case for AGR-produced results because of the generic reduction algorithms used in AGRs. An SPR often yields smaller results than AGRs for the language for which the SPR has customized reduction algorithms. But SPRs are not language-agnostic, and implementing a new SPR for a different language requires significant engineering efforts. This paper proposes Vulcan, a language-agnostic framework to further minimize AGRs-produced results by exploiting the formal syntax of the language to perform aggressive program transformations, in hope of creating reduction opportunities for other reduction algorithms to progress or even directly deleting bugirrelevant elements from the results. Our key insights are two-fold. First, the program transformations in all existing program reducers including SPRs are not diverse enough, which traps these program reducers early in 1-minimality. Second, compared with the original program, the results of AGRs are much smaller, and time-wise it is affordable to perform diverse program transformations that change programs but do not necessarily reduce the sizes of the programs directly. Within the Vulcan framework, we proposed three simple examples of fine-grained program transformations to demonstrate that Vulcan can indeed further push the 1-minimality of AGRs. By performing these program transformations, a 1-minimal program might become a non-1-minimal one that can be further reduced later. Our extensive evaluations on multilingual benchmarks including C, Rust and SMT-LIBv2 programs strongly demonstrate the effectiveness and generality of Vulcan. Vulcan outperforms the state-of-the-art language-agnostic program reducer Perses in size in all benchmarks: On average, the result of Vulcan contains 33.55%, 21.61%, and 31.34% fewer tokens than that of Perses on C, Rust, and SMT-LIBv2 subjects respectively. Vulcan can produce even smaller results if more reduction time is allocated. Moreover, for the C programs that are reduced by C-Reduce, Vulcan is even able to further minimize them by 10.07%.

Kinetic Mechanism Development for the Direct Reduction of Single Hematite Pellets in H2/CO Atmospheres

Increasing interest in the direct reduction process of iron ore has revived investigations on gaseous and heterogeneous iron oxides’ kinetics. Despite extensive studies on the reduction of iron oxides with pure hydrogen or syngas, the development of a generic reduction mechanism for iron oxides is still lacking. The conventional shrinking core model hardly distinguishes between transport and reaction processes, leading to biases or even errors in the kinetic models. In the present study, a porous solid model, which solves mass balances of the individual gas‐phase species and solid ones assuming spherical symmetry, is used for developing a heterogeneous kinetic mechanism accounting for different iron oxidation stages (Fe2O3, Fe3O4, FeO). It also accounts for carbon accumulation and cementite formation to model the carburization phenomena when using carbon‐containing reducing agents like syngas. The proposed generic mechanism successfully reproduces 49 experimental data sets from the literature for single iron oxide pellets’ isothermal reduction with syngas of varying hydrogen content up to pure hydrogen without any adjustment of its parameters. The model predictions are in excellent agreement with the experimental data. Finally, the carburization kinetics are explained, and the factors (e.g., temperature, hydrogen content) affecting the carbon deposition are analyzed.

Finite Entailment of Local Queries in the Z Family of Description Logics

In the last few years the field of logic-based knowledge representation took a lot of inspiration from database theory. A vital example is that the finite model semantics in description logics (DLs) is reconsidered as a desirable alternative to the classical one and that query entailment has replaced knowledge-base satisfiability (KBSat) checking as the key inference problem. However, despite the considerable effort, the overall picture concerning finite query answering in DLs is still incomplete. In this work we study the complexity of finite entailment of local queries (conjunctive queries and positive boolean combinations thereof) in the Z family of DLs, one of the most powerful KR formalisms, lying on the verge of decidability. Our main result is that the DLs ZOQ and ZOI are finitely controllable, i.e. that their finite and unrestricted entailment problems for local queries coincide. This allows us to reuse recently established upper bounds on querying these logics under the classical semantics. While we will not solve finite query entailment for the third main logic in the Z family, ZIQ, we provide a generic reduction from the finite entail- ment problem to the finite KBSat problem, working for ZIQ and some of its sublogics. Our proofs unify and solidify previously established results on finite satisfiability and finite query entailment for many known DLs.

Combining data reduction, MIP solver and iterated local search for generalized assignment

ABSTRACT This work is motivated by a memory allocation problem (MAP) in an embedded system which is modeled as a generalized assignment problem (GAP) with side constraints. Thus, this paper aims to design a fast and sufficiently accurate method for GAP that will be used in future research to obtain a solution for MAP. Since this solution barely satisfies the conflict constraints, it will be repaired and then improved using local search . In the current research, the proposed method for GAP combines data reduction, a MIP solver, and iterated local search (ILS). The generic data reduction procedure is based on useful information provided by applying subgradient optimization to the Lagrangian relaxation of the knapsack constraints. In practice, it can eliminate up to of GAP variables. The reduced GAP left by this procedure is small and sparse. Furthermore, its optimal solution can be easily extended to an optimal or near-optimal solution of GAP. An ILS metaheuristic is designed for solving the reduced GAP and the entire method is tested on a widely used benchmark of large and difficult instances. Its comparison with recently published methods shows that it is competitive in terms of solution quality; it is also by far the fastest.

Impossibility on the Schnorr Signature from the One-More DL Assumption in the Non-Programmable Random Oracle Model

The Schnorr signature is one of the representative signature schemes and its security was widely discussed. In the random oracle model (ROM), it is provable from the DL assumption, whereas there is negative circumstantial evidence in the standard model. Fleischhacker, Jager, and Schröder showed that the tight security of the Schnorr signature is unprovable from a strong cryptographic assumption, such as the One-More DL (OM-DL) assumption and the computational and decisional Diffie-Hellman assumption, in the ROM via a generic reduction as long as the underlying cryptographic assumption holds. However, it remains open whether or not the impossibility of the provable security of the Schnorr signature from a strong assumption via a non-tight and reasonable reduction. In this paper, we show that the security of the Schnorr signature is unprovable from the OM-DL assumption in the non-programmable ROM as long as the OM-DL assumption holds. Our impossibility result is proven via a non-tight Turing reduction.

A Multi-purpose Data Pre-processing Framework using Machine Learning for Enterprise Data Models

Growth in the data processing industry has automated decision making for various domains such as engineering, education and also many fields of research. The increased growth has also accelerated higher dependencies on the data driven business decisions on enterprise scale data models. The accuracy of such decisions solely depends on correctness of the data. In the recent past, a good number of data cleaning methods are projected by various research attempts. Nonetheless, most of these outcomes are criticized for higher generalness or higher specificness. Thus, the demand for multi-purpose, however domain specific, framework for enterprise scale data pre-processing is in demand in the recent time. Hence, this work proposes a novel framework for data cleaning method as missing value identification using the standard domain length with significantly reduced time complexity, domain specific outlier identification using customizable rule engine, detailed generic outlier reduction using double differential clustering and finally dimensionality reduction using the change percentage dependency mapping. The outcome from this framework is significantly impressive as the outliers and missing treatment showcases nearly 99% accuracy over benchmarked dataset.

On Tight Security Proofs for Schnorr Signatures

The Schnorr signature scheme is the most efficient signature scheme based on the discrete logarithm problem and a long line of research investigates the existence of a tight security reduction for this scheme in the random oracle model. Almost all recent works present lower tightness bounds and most recently Seurin EUROCRYPT 2012 showed that under certain assumptions the non-tight security proof for Schnorr signatures in the random oracle by Pointcheval and Stern EUROCRYPT’96 is essentially optimal. All previous works in this direction rule out tight reductions from the (one-more) discrete logarithm problem. In this paper, we introduce a new meta-reduction technique, which shows lower bounds for the large and very natural class of generic reductions. A generic reduction is independent of a particular representation of group elements. Most reductions in state-of-the-art security proofs have this property. It is desirable, because then the reduction applies generically to any concrete instantiation of the group. Our approach shows unconditionally that there is no tight generic reduction from any natural non-interactive computational problem $$\Pi $$ defined over algebraic groups to breaking Schnorr signatures, unless solving $$\Pi $$ is easy. In an additional application of the new meta-reduction technique, we also unconditionally rule out any (even non-tight) generic reduction from natural non-interactive computational problems defined over algebraic groups to breaking Schnorr signatures in the non-programmable random oracle model.

Kernels for (Connected) Dominating Set on Graphs with Excluded Topological Minors

We give the first linear kernels for the D ominating S et and C onnected D ominating S et problems on graphs excluding a fixed graph H as a topological minor. In other words, we prove the existence of polynomial time algorithms that, for a given H -topological-minor-free graph G and a positive integer k , output an H -topological-minor-free graph G ′ on O ( k ) vertices such that G has a (connected) dominating set of size k if and only if G ′ has one. Our results extend the known classes of graphs on which the D ominating S et and C onnected D ominating S et problems admit linear kernels. Prior to our work, it was known that these problems admit linear kernels on graphs excluding a fixed apex graph H as a minor. Moreover, for D ominating S et , a kernel of size k c ( H ) , where c ( H ) is a constant depending on the size of H , follows from a more general result on the kernelization of D ominating S et on graphs of bounded degeneracy. Alon and Gutner explicitly asked whether one can obtain a linear kernel for D ominating S et on H -minor-free graphs. We answer this question in the affirmative and in fact prove a more general result. For C onnected D ominating S et no polynomial kernel even on H -minor-free graphs was known prior to our work. On the negative side, it is known that C onnected D ominating S et on 2-degenerated graphs does not admit a polynomial kernel unless coNP ⊆ NP/poly. Our kernelization algorithm is based on a non-trivial combination of the following ingredients • The structural theorem of Grohe and Marx [STOC 2012] for graphs excluding a fixed graph H as a topological minor; • A novel notion of protrusions, different than the one defined in [FOCS 2009]; • Our results are based on a generic reduction rule that produces an equivalent instance (in case the input graph is H -minor-free) of the problem, with treewidth O (√ k ). The application of this rule in a divide-and-conquer fashion, together with the new notion of protrusions, gives us the linear kernels. A protrusion in a graph [FOCS 2009] is a subgraph of constant treewidth which is separated from the rest of the graph by at most a constant number of vertices. In our variant of protrusions, instead of stipulating that the subgraph be of constant treewidth , we ask that it contains a constant number of vertices from a solution . We believe that this new take on protrusions would be useful for other graph problems and in different algorithmic settings.

Quantum interference by localized scattering waves of gapless helical modes in narrow strips of topological insulators

Quantum interference in scattering from a potential offset is investigated in narrow strips of two-dimensional systems described by the Bernevig-Hughes-Zhang Hamiltonian. Attention is focused on the situations where the transmission in the scattering region takes place around the Dirac point of topological insulators when the hybridization energy gap is eliminated by utilizing transverse interference. Apart from conventional periodic transmission modulation that takes place when the length of the potential offset region is varied, resonant disappearances of reflection occur for short potential offsets. The anomalous resonance appears not only for the four-band Hamiltonian but also for the two-band Hamiltonian, manifesting the generality of the phenomenon. Evanescent-like waves excited around the potential steps are indicated to be responsible for the anomalous behavior. The interference states can couple with each other and generic reduction in the amplitude of transmission modulation occurs upon coupling with the periodic modulation.

THE GENERIC DEGREES OF DENSITY-1 SETS, AND A CHARACTERIZATION OF THE HYPERARITHMETIC REALS

AbstractA generic computation of a subsetAof ℕ is a computation which correctly computes most of the bits ofA, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory, where it has been noticed that frequently, it is more important to know how difficult a type of problem is in the general case than how difficult it is in the worst case. When we study this concept from a recursion theoretic point of view, to create a transitive relationship, we are forced to consider oracles that sometimes fail to give answers when asked questions. Unfortunately, this makes working in the generic degrees quite difficult. Indeed, we show that generic reduction is$\Pi _1^1$―complete. To help avoid this difficulty, we work with the generic degrees of density-1 reals. We demonstrate how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees, and we also use these density-1 sets to provide a new a characterization of the hyperartithmetical Turing degrees.

Scheduling in Wireless Networks with Rayleigh-Fading Interference

We study approximation algorithms for optimization of wireless spectrum access with n communication requests when interference conditions are given by the Rayleigh-fading model. This model extends the deterministic interference model based on the signal-to-interference-plus-noise ratio (SINR) using stochastic propagation to address fading effects observed in reality. We consider worst-case approximation guarantees for the two standard problems of capacity maximization and latency minimization. Our main result is a generic reduction of Rayleigh fading to the deterministic non-fading model. It allows to apply existing algorithms for the non-fading model in the Rayleigh-fading scenario while losing only a factor of O(log* n) in the approximation guarantee. This way, we obtain the first approximation guarantees for Rayleigh fading and, more fundamentally, show that non-trivial stochastic fading effects can be successfully handled using existing and future techniques for the non-fading model. We generalize these results in two ways. First, the same results apply for capacity maximization with variable data rates, when links obtain (non-binary) utility depending on the achieved SINR. Second, for binary utilities, we use a more detailed argument to obtain similar results even for distributed and game-theoretic approaches. Our analytical treatment is supported by simulations illustrating the performance of regret learning and, more generally, the relationship between both models.

Performance of correlation approaches for the evaluation of spatial distortion reductions

The analysis of optical remote sensing images often requires a perfect pixel alignment between single bands. Even smallest deviations may degrade the accuracy of subsequent parameter retrieval or lead to the detection of non-existing structures caused by artificial gradients. Hence, a careful pre-processing is essential for minimizing spatial non-uniformities such as erroneous co-registration. The results need to be validated and assigned with a quality flag that is unfortunately still not a common practice. In this letter, four broadly used global correlation approaches, a two-dimensional Gaussian peak fit, a poly phase technique, an iterative phase approach and its proposed enhancement, were tested for their capacity to serve either as an evaluation tool for preceding spatial distortion reductions, e.g. by co-registration, or as a global minimizer for generic reduction approaches. For this eight broadly used test images, three Landsat 7 and three Landsat 8 samples were sub pixel shifted artificially and degraded by different noise levels resulting in more than 200,000 noise and shift scenarios. Additionally, one state-of-the-art approach was enhanced by 50% on average for all scenarios and by 280% on average for all non-degraded images. This study indicates that three out of four approaches can serve as evaluation tools for spatial distortion reductions or as a global minimizer even for highly degraded images, whereas proposed enhancement offers highest accuracy and the poly phase approach offers best overall performance with regard to considered criteria.

THELI: CONVENIENT REDUCTION OF OPTICAL, NEAR-INFRARED, AND MID-INFRARED IMAGING DATA

The last 15 years have seen a surge of new multi-chip optical and near-IR imagers. While some of them are accompanied by specific reduction pipelines, user-friendly and generic reduction tools are uncommon. In this paper I introduce THELI, an easy-to-use graphical interface driving an end-to-end pipeline for the reduction of any optical, near-IR and mid-IR imaging data. The advantages of THELI when compared to other approaches are highlighted. Combining a multitude of processing algorithms and third party software, THELI provides researchers with a single, homogeneous tool. A short learning curve ensures quick success for new and more experienced observers alike. All tasks are largely automated, while at the same time a high level of flexibility and alternative reduction schemes ensure that widely different scientific requirements can be met. Over 90 optical and infrared instruments at observatories world-wide are pre-configured, while more can be added by the user. The online Appendices contain three walk-through examples using public data (optical, near-IR and mid-IR). Additional extensive online documentation is available for training and troubleshooting.

On the Competitive Ratio of Online Sampling Auctions

We study online profit-maximizing auctions for digital goods with adversarial bid selection and uniformly random arrivals; in this sense, our model lies at the intersection of prior-free mechanism design and secretary problems. Our goal is to design auctions that are constant competitive with F (2) . We give a generic reduction that transforms any offline auction to an online one with only a loss of a factor of 2 in the competitive ratio. We also present some natural auctions, both randomized and deterministic, and study their competitive ratio. Our analysis reveals some interesting connections of one of these auctions with RSOP.

Computing and counting longest paths on circular-arc graphs in polynomial time

The longest path problem asks for a path with the largest number of vertices in a given graph. In contrast to the Hamiltonian path problem, until recently polynomial algorithms for the longest path problem were known only for small graph classes, such as trees. Recently, a polynomial algorithm for this problem on interval graphs has been presented in Ioannidou et al. (2011) [19] with running time O(n4) on a graph with n vertices, thus answering the open question posed in Uehara and Uno (2004) [32]. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect; for instance, several problems– e.g. coloring –are NP-hard on circular-arc graphs, although they can be efficiently solved on interval graphs. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs. In addition, by exploiting deeper the structure of circular-arc graphs, we manage to get rid of the linear time overhead of the reduction, and thus this algorithm turns out to have the same running time O(n4) as the one on interval graphs. Our algorithm, which significantly simplifies the approach of Ioannidou et al. (2011) [19], computes in the same time an n-approximation of the (exponentially large in worst case) number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, in contrast to Ioannidou et al. (2011) [19], this algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight.

Rapid enumeration within a fraction of a single glance: The role of visible persistence in object individuation capacity

The number of items that can be individuated at a single glance is limited. Here, we investigate object individuation at a higher temporal resolution, in fractions of a single glance. In two experiments involving object individuation we manipulated the duration of visual persistence of the target items with a forward masking procedure. The number of items as well as their stimulus–onset asynchrony (SOA) to the mask was varied independently. The results showed main effects of numerosity and SOA, as well as an interaction. These effects were not caused by a generic reduction of item visibility by the mask. Instead, the SOA manipulation appeared to fractionate the time to access the sensory image. These findings suggest that the capacity limit of 3–4 items found in object individuation is, at least partially, the consequence of the temporal window of access to sensory information.

Computing and Counting Longest Paths on Circular-Arc Graphs in Polynomial Time

The longest path problem asks for a path with the largest number of vertices in a given graph. The first polynomial time algorithm (with running time O(n4)) has been recently developed for interval graphs. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs, which turns out to have the same running time O(n4) with the one on interval graphs, as we manage to get rid of the linear overhead of the reduction. This algorithm computes in the same time an n-approximation of the number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, our algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight.

Numerical study of the influence of the atmospheric pressure on the heat and mass transfer rates of desiccant wheels

A study was conducted to investigate the influence of the atmospheric pressure, from 101,325 to 60,000Pa (corresponding from 0 to 4217m of altitude), on the heat and mass transfer rates of desiccant wheels (hygroscopic matrix of silica gel RD), assuming fixed-mass airflow rates and fixed inlet states for the process and regeneration airflows, defined by the respective inlet temperatures and water vapour contents. The results show a generic reduction of the heat and mass transfer rates as the atmospheric pressure decreases, an effect that is more pronounced for short channel wheels and high airflow rates. Correlations based on the numerical results are presented for the correction of the heat and mass transfer rates when the desiccant wheels are operating at non-standard atmospheric pressure.