Dual Version Research Articles

TILTING COMPLEXES AND CODIMENSION FUNCTIONS OVER COMMUTATIVE NOETHERIAN RINGS

AbstractIn the derived category of a commutative noetherian ring, we explicitly construct a silting object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” condition. Our new construction is based on local cohomology and it allows us to study when the silting object is tilting. For a ring admitting a dualizing complex, this occurs precisely when the sp-filtration arises from a codimension function on the spectrum. In the absence of a dualizing complex, the situation is more delicate and the tilting property is closely related to the condition that the ring is a homomorphic image of a Cohen–Macaulay ring. We also provide dual versions of our results in the cosilting case.

Tropical Fock–Goncharov coordinates for -webs on surfaces I: construction

Abstract For a finite-type surface $\mathfrak {S}$ , we study a preferred basis for the commutative algebra $\mathbb {C}[\mathscr {R}_{\mathrm {SL}_3(\mathbb {C})}(\mathfrak {S})]$ of regular functions on the $\mathrm {SL}_3(\mathbb {C})$ -character variety, introduced by Sikora–Westbury. These basis elements come from the trace functions associated to certain trivalent graphs embedded in the surface $\mathfrak {S}$ . We show that this basis can be naturally indexed by nonnegative integer coordinates, defined by Knutson–Tao rhombus inequalities and modulo 3 congruence conditions. These coordinates are related, by the geometric theory of Fock and Goncharov, to the tropical points at infinity of the dual version of the character variety.

Affine isoperimetric inequalities on flag manifolds

Abstract Building on work of Furstenberg and Tzkoni, we introduce $\mathbf {r}$ -flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the Grassmannian can be considered as a special case). We establish affine and linear invariance properties and extend fundamental results to this new setting. In particular, we prove several affine isoperimetric inequalities from convex geometry and their approximate reverse forms. We also introduce functional forms of these quantities and establish corresponding inequalities.

Memristor neurons and their coupling networks based on Edge of Chaos Kernel

Chua's theory of local activity shows that local activity is the origin of complexity, and the complexity can only occur on or near the stable locally active domain, referred to as Edge of Chaos (EOC). Very recently, for the voltage-controlled locally active memristors, a new physical concept dubbed “Edge of Chaos Kernel” (EOCK), which consists of a series combination between a negative resistance and a negative inductance and exhibits the EOC phenomenon of being stable yet potentially unstable, was defined and applied to the Hodgkin-Huxley neural circuit model. When an EOCK is coupled to a passive environment, its stability is disrupted, resulting in the emergence of action potentials, chaos and various complex phenomena. This paper proposes the dual version of the EOCK called as R-C EOCK, which consists of the parallel combination between a negative resistance and a negative capacitance. We show that the actual NbO memristor manufactured by NaMLab essentially belongs to a current-controlled locally active memristor which contains a R-C EOCK and gives the signature of its EOCK and EOC. We construct a second-order neuron based on the NbO memristor when connected in parallel with a passive capacitor, and further prove that only memristors endowed with an EOCK can generate action potential. On this basis, we construct a minimum cellular neural network with only 7 components based on two NbO memristor neurons and a passive coupling resistor, in which neuromorphic behaviors of static and dynamic pattern formation may emerge if and only if the single neuron has an EOCK and is poised on the EOC. The analysis in this paper explains the dynamic mechanism of Smale's paradox, in which two mathematically dead neurons coupled by a passive environment may become alive, under the same or different input current excitation, which are more in line with the actual biological neural networks.

On the Parallel Parameterized Complexity of MaxSAT Variants

In the maximum satisfiability problem (max-sat) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of various versions of max-sat and provide the first constant-time algorithms parameterized either by the solution size or by the allowed excess relative to some guarantee. For the dual parameterized version where the parameter is the number of clauses we are allowed to leave unsatisfied, we present the first parallel algorithm for max-2sat (known as almost-2sat). The difficulty in solving almost-2sat in parallel comes from the fact that the iterative compression method, originally developed to prove that the problem is fixed-parameter tractable at all, is inherently sequential. We observe that a graph flow whose value is a parameter can be computed in parallel and develop a parallel algorithm for the vertex cover problem parameterized above the size of a given matching. Finally, we study the parallel complexity of max-sat parameterized by the vertex cover number, the treedepth, the feedback vertex set number, and the treewidth of the input’s incidence graph. While max-sat is fixedparameter tractable for all of these parameters, we show that they allow different degrees of possible parallelization. For all four we develop dedicated parallel algorithms that are constructive, meaning that they output an optimal assignment – in contrast to results that can be obtained by parallel meta-theorems, which often only solve the decision version.

Symbolic group varieties and dual surjunctivity

Let G be a group. Let X be an algebraic group over an algebraically closed field K . Denote by A=X(K) the set of rational points of X . We study algebraic group cellular automata \tau \colon A^G \to A^G whose local defining map is induced by a homomorphism of algebraic groups X^M \to X , where M is a finite memory. When G is sofic and K is uncountable, we show that if \tau is post-surjective, then it is weakly pre-injective. Our result extends the dual version of Gottschalk's conjecture for finite alphabets proposed by Capobianco, Kari, and Taati. When G is amenable, we prove that if \tau is surjective, then it is weakly pre-injective, and conversely, if \tau is pre-injective, then it is surjective. Hence, we obtain a complete answer to a question of Gromov on the Garden of Eden theorem in the case of algebraic group cellular automata.

Fractional covers of hypergraphs with bounded multi-intersection

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. We show how this combinatorial result can be used to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is ≤k for some constant k. Moreover, we show a dual version of our main result for fractional hitting sets.

Optimal releasing strategy of enterprise software firms facing the competition from cloud providers

In the contemporary enterprise software market, there has been a notable surge in the utilization of SaaS products. This trend has prompted certain upstream suppliers of cloud resources, commonly referred to as cloud providers, to introduce their own SaaS offerings, thereby augmenting the competition within the industry. The matter of optimal releasing strategy encountered by software firms in this industry has been scarcely addressed in prior literature. Therefore, the present study employs the Hotelling model to depict the market segmentation in the context of a software firm’s selection among three distinct strategies, namely on-premise, SaaS, and dual version strategies, to effectively manage competition. Through an examination of the optimal pricing and profit for each strategy, and a subsequent analysis of the resulting profits, we have managed to arrive at conclusive recommendations for optimal strategy selection. Based on the analytical findings, it can be inferred that the selection of the optimal strategy can be classified into two distinct scenarios, which are contingent upon the magnitude of the unit cloud rental fee. In a high-cost rental environment, the optimal release strategy shifts from the SaaS strategy and dual version strategy to the on-premise strategy, as the disparity in value between on-premise and SaaS versions increases. In a context of low rental fee and a widening value gap, the optimal strategy choice sequence is as follows: SaaS, on-premise, dual version, on-premise, dual version, and ultimately on-premise. Furthermore, we analyze and reveal the impact of various factors on the maximum profit that software companies can achieve. The findings we have derived have significant implications for software companies’ decision-making in the face of the challenge posed by highly centralized public cloud supply.

Diluting the patriarchal dominance: Review of Developing Feminist Discourse in Pakistani Context

The present study is aimed to review of the development of feminist critical discourse in Pakistani context. It is considered that Pakistan is an Islamic country and there is a misperception in the Western world that women are oppressed in Pakistan on the name of Islam. This article provides a review of the dual version of female oppression in Pakistani context i.e. religious and cultural. The very first perception of women oppression in Pakistan by the western world is wrong as Pakistan as an Islamic ideological state does not oppress women rather guarantees their equal rights. In this regards there is a long list of legal development for the protection of the rights of women. The second kind of oppression is the cultural oppression against women. There are a lot of cultural practices in different regions of Pakistan which are oppressive towards women like Wata Sata, dowry death and forced marriages. The data for the present study has been reviewed as per available academic resources and research journals. The significance of the study is to counter western misunderstanding about the female oppression in Pakistani context. While at the same time the study is significant as it raises voice against the prevalent cultural practices of oppression against women in Pakistan. The findings of the present study reveal that there is a development of feminist critical discourse which is diluting the patriarchal dominance that is maintained through cultural practices in Pakistan.

Real-time forecasting of time series in financial markets using sequentially trained dual-LSTMs

Financial markets are highly complex and volatile; thus, accurate forecasting of such markets is vital to make early alerts about crashes and subsequent recoveries. People have been using learning tools from diverse fields such as financial mathematics and machine learning to make trustworthy forecasting on such markets. However, the accuracy of such techniques had not been adequate until artificial neural network frameworks such as long short-term memory (LSTM) were utilized. Moreover, making accurate real-time forecasting, also known as nowcasting, of financial time series is highly subjective to the LSTM’s architecture in use and the procedure of training it. Herein, we forecast financial markets in real-time by training a dual version of LSTM which forecasts only one time step at each iteration so that the forecast for this iteration will be in the input for the next iteration. Semi-convergence is a prominent issue in a recurrent LSTM setup as the error could propagate through iterations; however, the duality of this LSTM aids in dwindling this issue. Especially, we employ one LSTM to find the best number of epochs associated with the least loss and train the second LSTM only through that many epochs to make forecasting. We treat the current forecast as a part of the training set for the next forecast and train the same LSTM. While classic ways of training cause more error when the forecast is made further away through the test period, our approach offers superior accuracy as the training increases when it proceeds through the testing period. The forecasting accuracy of our approach is validated using three time series from each of the three diverse financial markets: stock, cryptocurrency, and commodity. The results are compared with those of a single LSTM, an extended Kalman filter, and an autoregressive integrated moving average model.

Centers of Hecke algebras of complex reflection groups

We provide a dual version of the Geck–Rouquier Theorem (Geck and Rouquier in Finite Reductive Groups (Luminy, 1994), Progr. Math., vol. 141, Birkhäuser Boston, Boston, pp. 251–272, 1997) on the center of an Iwahori–Hecke algebra, which also covers the complex case. For the eight complex reflection groups of rank 2, for which the symmetrising trace conjecture is known to be true, we provide a new faithful matrix model for their Hecke algebra H. These models enable concrete calculations inside H. For each of the eight groups, we compute an explicit integral basis of the center of H.

Reducing the Problem of the Modal Control by Output for Stationary Fourth-Order Systems with Two Inputs and Two Outputs to the Control by State for a System with a Single Input

A problem of modal control by output for fourth-order dynamical systems with two inputs and two outputs is presented. For a certain class of such systems, an approach is proposed for reducing the problem under consideration to a control (direct version) or observation (dual version) problem for a system with a single input. The approach is based on two successive similarity transformations of the closed-loop system with a controller by output, which make it possible to reset one of the rows of the controller matrix by state or one of the columns of the observer matrix. The class of systems for which the condition of such zeroing is simultaneously a condition for the existence of an output controller is studied. Theorems on the inequality of the indices of controllability and observability in the system under the conditions presented are proved. A variant of using the well-known Bass–Gura and Ackermann formulas is proposed, which significantly simplifies the symbolic expressions for the controller (observer) in the transformed system. Examples of the application of the proposed approach, both in the direct and in the dual version, are considered. Symbolic calculations in MATLAB validate the results.

Comparison of single taper and dual taper versions of the same stem design in total hip arthroplasty for primary osteoarthritis

BackgroundIn total hip arthroplasty (THA), the outcomes of single taper (ST) and dual taper (DT) versions of the same stem design have been scarcely studied. A registry study comparing ST and DT versions of the same stem design was designed, aiming to assess: (1) the survival rates and the hazard ratios for failure; (2) the survival rates and the hazard ratios for failure using stem-focused endpoints.Material and methodsA regional arthroplasty registry was interrogated about stem designs with ST and DT versions in cementless THAs performed for primary osteoarthritis. Only the same cup and ceramic-on-ceramic bearings were included: the DT stems had a titanium-on-titanium modularity. Demographic and implant features were recorded. Survival rates and hazard ratios were evaluated and compared. Stem-focused endpoints were also investigated.ResultsA total of 5359 THAs were included, with three stem designs. The two versions of every stem showed different demographics and implant-related features: ST versions were preferentially implanted in heavier young men. For each stem, the two versions had similar survival rates at 5 years (p = 0.076; p = 0.319; p = 0.616) and similar adjusted hazard ratios for failures (p = 0.084; p = 0.308; p = 0.729). When stem-focused endpoints were adopted, the ST and DT versions of the three stems achieved similar survival rates (p = 0.710; p = 0.784; p = 0.983) and similar adjusted hazard ratios (p = 0.647; p = 0.858; p = 0.787). Three neck breakages occurred (0.0007% of all the modular implants).ConclusionsST and DT versions of the same stem design did not show any differences in terms of survival rates and hazard ratios for failures at 5 years.LEVEL OF EVIDENCE: IV.

On Parametric and Matrix Solutions to the Diophantine Equation x2 + dy2 − z2 = 0 Where d Is a Positive Square‐Free Integer

The well‐known matrix‐generated tree structure for Pythagorean triplets is extended to the primitive solutions of the Diophantine equation x2 + dy2 − z2 = 0 where d is a positive square‐free integer. The proof is based on a parametrization of these solutions as well as on a dual version of the Fermat’s method of descent.

Exploiting HBM on FPGAs for Data Processing

Field Programmable Gate Arrays (FPGAs) are increasingly being used in data centers and the cloud due to their potential to accelerate certain workloads as well as for their architectural flexibility, since they can be used as accelerators, smart-NICs, or stand-alone processors. To meet the challenges posed by these new use cases, FPGAs are quickly evolving in terms of their capabilities and organization. The utilization of High Bandwidth Memory (HBM) in FPGA devices is one recent example of such a trend. In this article, we study the potential of FPGAs equipped with HBM from a data analytics perspective. We consider three workloads common in analytics-oriented databases and implement them on an FPGA showing in which cases they benefit from HBM: range selection, hash join, and stochastic gradient descent for linear model training. We integrate our designs into a columnar database (MonetDB) and show the trade-offs arising from the integration related to data movement and partitioning. We consider two possible configurations of the HBM, using a single and a dual clock version design. With the right design, FPGA+HBM-based solutions are able to surpass the highest performance provided by either a two-socket POWER9 1 system or a 14-core Xeon 2 E5 by up to 5.9× (range selection), 18.3× (hash join), and 6.1× (SGD).

On dual surjunctivity and applications

We explore the dual version of Gottschalk’s conjecture recently introduced by Capobianco, Kari, and Taati, and the notion of dual surjunctivity in general. We show that dual surjunctive groups satisfy Kaplansky’s direct finiteness conjecture for all fields of positive characteristic. By quantifying the notions of injectivity and post-surjectivity for cellular automata, we show that the image of the full topological shift under an injective cellular automaton is a subshift of finite type in a quantitative way. Moreover, we show that dual surjunctive groups are closed under ultraproducts, under elementary equivalence, and under certain semidirect products (using the ideas of Arzhantseva and Gal for the latter); they form a closed subset in the space of marked groups, fully residually dual surjunctive groups are dual surjunctive, etc. We also consider dual surjunctive systems for more general dynamical systems, namely for certain expansive algebraic actions, employing results of Chung and Li.

Intelligent System Application in Clinical Management of Medical Teaching Based on Deep Reinforcement Learning

When dealing with engineering projects, there are many kinds of planning schemes. There are many problems to be solved in the performance and economic conditions of these indicators and engineering contents we study. Recently, many researchers have made great achievements in optimizing various subject projects. One of its purposes is to optimize and improve intelligent multi-objectives to make it more effective. Therefore, it is of great significance to develop intelligent multi-objective projects in academia and more engineering fields. The purpose of this study is to make efforts to strengthen the learning and construction of rapidly developing multi-objective optimization programs, and closely link these programs with neural network, fuzzy technology, interactive technology, and give a lot of examples of multi-objective optimization improvement program methods, which can eliminate the uncertainty in the multi-objective project plan, The purpose is to solve some difficult problems of multi-objective optimization and give the best suggestions. In this study, the strengthening of learning construction is combined with the clinical experiment, and most of this teaching method is put in the clinical management experiment of medical teaching. At the end of this study, we compared the performance of deep reinforcement learning with its dual structure version and interleaved structure version in different medical teaching clinical management environments and make a detailed analysis. Deep reinforcement learning provides a new idea for the improvement of intelligent multi-objective optimization and clinical management of medical teaching.

Dual Relativistic Quantum Mechanics I

In \cite{2} it was shown that Einstein's special theory of relativity and Maxwell's field theory have mathematically equivalent dual versions. The dual versions arise from an identity relating observer time to proper time as a contact transformation on configuration space, which leaves phase space invariant. The special theory has a dual version in the sense that, for any set of $n$ particles, every observer has two unique sets of global variables $({\bf{X}}, t)$ and $({\bf{X}}, \tau)$ to describe the dynamics, where ${\bf{X}}$ is the (unique) canonical center of mass. In the $({\bf{X}}, t)$ variables, time is relative and the speed of light is unique, while in the $({\bf{X}}, \tau)$ variables, time is unique and the speed of light is relative with no upper bound. In the Maxwell case, the two sets of particle wave equations are not equivalent. The dual version contains an additional longitudinal (dissipative) radiation term that appears instantaneously with acceleration, leading to the prediction that radiation from a betatron (of any frequency) will not produce photoelectrons. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein's special theory of relativity, without a self-energy divergency, or need of the problematic Lorentz-Dirac equation or any assumptions about the size or structure of a particle. The purpose of this paper is to introduce and develop the dual theory of relativistic quantum mechanics. We obtain three distinct dual relativistic wave equations that reduce to the Schr{\"o}dinger equation when minimal coupling is turned off. We show that the dual Dirac equation provides a new formula for the anomalous magnetic moment of a charged particle. We can obtain the exact value for the electron g-factor and phenomenological values for the muon and proton g-factors.

Maximal Perimeters of Polytope Sections and Origin-Symmetry

Let $$P\subset {\mathbb {R}}^n$$ $$(n\ge 3)$$ be a convex polytope containing the origin in its interior. Let $${\text {vol}}_{n-2}({{\text {relbd}}(P\cap \lbrace t\xi + \xi ^\perp \rbrace )})$$ denote the $$(n-2)$$ -dimensional volume of the relative boundary of $$P\cap \lbrace t\xi + \xi ^\perp \rbrace $$ for $$t\in {\mathbb {R}}$$ , $$\xi \in S^{n-1}$$ . We prove the following: if $$\begin{aligned} {\text {vol}}_{n-2}({{\text {relbd}}(P\cap \xi ^\perp )}) =\max _{t\in {\mathbb {R}}}\,{\text {vol}}_{n-2}({{\text {relbd}}(P\cap \lbrace t\xi + \xi ^\perp \rbrace )}) \end{aligned}$$ for all $$\xi \in S^{n-1}$$ , then P is origin-symmetric, i.e., $$P=-P$$ . Our result gives a partial affirmative answer to a conjecture by Makai et al. We also characterize the origin-symmetry of $$C^2$$ star bodies in terms of the dual quermassintegrals of their sections; this can be seen as a dual version of the conjecture of Makai et al.

The socle tableau as a dual version of the Littlewood–Richardson tableau

Like the LR-tableau, a socle tableau is given as a skew diagram with certain entries. Unlike in the LR-tableau, the entries in the socle tableau are weakly increasing in each row, strictly increasing in each column and satisfy a modified lattice permutation property. In the study of embeddings of a subgroup in a finite abelian p $p$ -group, socle tableaux occur as isomorphism invariants, they are given by the socle series of the subgroup. We show that each socle tableau can be realized by some embedding. Moreover, the socle tableau of an embedding and the LR-tableau of the dual embedding determine each other — a correspondence which appears to be related to the tableau switching studied by Benkart, Sottile and Stroomer. We illustrate how the entries in the socle tableau position the object within the Auslander–Reiten quiver. Like the LR-tableau, the socle tableau determines the irreducible component of the object in representation space.