Combinatorial Device Research Articles

Traveling salesman problem solution using magnonic combinatorial device

Traveling salesman problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number of possible routes. In this work, we describe a special type of hardware for the TSP solution. It is a magnonic combinatorial device comprising magnetic and electric parts connected in the active ring circuit. There is a number of possible propagation routes in the magnetic mesh made of phase shifters, frequency filters, and attenuators. The phase shifters mimic cities in TSP while the distance between the cities is encoded in the signal attenuation. The set of frequency filters makes the waves on different frequencies propagate through the different routes. The principle of operation is based on the classical wave superposition. There is a number of waves coming in all possible routes in parallel accumulating different phase shifts and amplitude damping. However, only the wave(s) that accumulates the certain phase shift will be amplified by the electric part. The amplification comes first to the waves that possess the minimum propagation losses. It makes this type of device suitable for TSP solution, where waves are similar to the salesmen traveling in all possible routes at a time. We present the results of numerical modeling illustrating the TSP solutions for four and six cities. Also, we present experimental data for the TSP solution with four cities. The prototype device is built of commercially available components including magnetic phase shifters/filters, coaxial cables, splitters, attenuators, and a broadband amplifier. There are three examples of finding the shortest route between the cities for three different sets of city-to-city distances. The proposed approach is scalable to TSP with a larger number of cities. Physical limits and challenges are also discussed.

Ten-kilohertz two-photon microscopy imaging of single-cell dendritic activity and hemodynamics in vivo.

The studying of rapid neuronal signaling across large spatial scales in intact, living brains requires both high temporal resolution and versatility of the measurement device. We introduce a high-speed two-photon microscope based on a custom-built acousto-optic deflector (AOD). This microscope has a maximum line scan frequency of 400kHz and a maximum frame rate of 10,000 frames per second (fps) at . For stepwise magnification from population view to subcellular view with high spatial and temporal resolution, we combined the AOD with resonance-galvo (RS) scanning. With this combinatorial device that supports both large-view navigation and small-view high-speed imaging, we measured dendritic calcium propagation velocity and the velocity of single red blood cells (RBCs). We measured dendritic calcium propagation velocity ( ) in OGB-1-labeled single cortical neurons in mice in vivo. To benchmark the spatial precision and detection sensitivity of measurement in vivo, we also visualized the trajectories of single RBCs and found that their movement speed follows Poiseuille's law of laminar flow. This proof-of-concept methodological development shows that the combination of AOD and RS scanning two-photon microscopy provides both versatility and precision for quantitative analysis of single neuronal activities and hemodynamics in vivo.

Yttrium Iron Garnet-Based Combinatorial Logic and Memory Devices

Yttrium iron garnet Y₃Fe₂(FeO₄)₃ (YIG) has a uniquely low magnetic damping for spin waves, which makes it a perfect material for magnonic devices. Spin waves typically exist in the microwave frequency range and their wavelength can be decreased to the nanoscale. Their dispersion in YIG waveguides depends on the strength and orientation of the bias magnetic field. It may be possible to exploit YIG waveguides as field-controlled filters and delay lines. In this work, we describe combinatorial logic and memory devices to benefit YIG properties. An act of computation in the combinatorial device is associated with finding a route connecting the input and output ports. We present experimental data demonstrating the pathfinding in the active ring circuit with YIG waveguide. The ability to search in parallel through multiple paths is the most appealing property of combinatorial devices. Potentially, they may compete with quantum computers in functional throughput.

Instantaneous in‐band radio frequency interference suppression using non‐linear folders

A front-end adaptive folder with a filter is presented to instantaneously push jammers to higher frequencies while preserving the integrity of small signals of interest. A programmable filter is utilised to further suppress folded jammers for achieving a widely scalable dynamic range over a large frequency range. To achieve maximum programmability with a minimal increase of power and area, combinatorial intrinsic device characteristics are exploited to tune folding points for rapid adaptation to a changing electromagnetic environment.

On handle theory for Morse–Bott critical manifolds

In this article, we use Conley Index Theory to set up a framework to associate topological-dynamical invariants to a Morse–Bott flow in a neighborhood of a critical manifold. Isolating blocks N for a critical manifold S are characterized in terms of conditions on the ranks of its homology Conley index. The necessity of these conditions follows from the generalized Morse–Bott inequalities for isolating blocks. Morse–Bott semi-graphs turn out to be a useful combinatorial device to record these topological conditions. One goal is to verify that these conditions when imposed on an n-abstract Morse–Bott semi-graph are sufficient for its realization. This is attained by introducing Morse–Bott handle surgeries in order to construct isolating blocks for critical manifolds in dimensions 2 and 3, and for a large class in higher dimensions. Stronger results are obtained in dimensions 2 and 3 where necessary and sufficient conditions for a Morse–Bott graph to be associated to a Morse–Bott flow on some manifold M are determined.

Self‐similar sets, simple augmented trees and their Lipschitz equivalence

Given an iterated function system (IFS) of contractive similitudes, the theory of Gromov hyperbolic graph on the IFS has been established recently. In the paper, we introduce a notion of simple augmented tree which is a Gromov hyperbolic graph. By generalizing a combinatorial device of rearrangeable matrix, we show that there exists a near-isometry between the simple augmented tree and the symbolic space of the IFS, so that their hyperbolic boundaries are Lipschitz equivalent. We then apply this to consider the Lipschitz equivalence of self-similar sets with or without assuming the open set condition. Moreover, we also provide a criterion for a self-similar set to be a Cantor-type set which completely answers an open question raised in \cite{LaLu13}. Our study extends the previous works.

Application of super-sticking algebraic operation of variables for Boolean functions minimization by combinatorial method

The simplification of the problem of Boolean function minimization by a combinatorial method is a new procedure for the algebra of logic – super-sticking of variables. This procedure is performed if there is a complete binary combinatorial system with repetition or an incomplete binary combinatorial system with repetition in the truth table structure. The procedure for reducing the total perfect disjunctive normal form (PDNF) of the logical function gives unity. And since the complete PDNF uniquely determines the complete binary combinatorial system with repetition and vice versa, this gives grounds to delete all the blocks of the complete binary combinatorial system from the truth table, whose structure allows to carry out the rules of super-sticking of variables. The efficiency of the algebraic operation of supers-sticking of variables greatly simplifies the algorithm for Boolean function minimization and allows manual minimization of functions with a number of variables up to 10. The complexity of the algorithm for finding the minimal function by a combinatorial method is O(n) and is linear for n<7. With an increase in the number of variables from n=6 to 8, the growth dynamics of the number of transformations is characterized by the law O(n 2 ), followed by the growth of O(f(n)) with the increase in the Boolean function capacity according to the polynomial law. The introduction of an algebraic operation of super-sticking of variables to the problem of Boolean function minimization is more advantageous in comparison with analogs in the following factors: – lower cost of development and implementation, since a significant proportion of functions are minimized by functions with a number of variables of no more than 16, and therefore, in general, the need for automation of the process of minimizing the function decreases; – increase in manual minimization of 4–10 bit functions, facilitates control and study of the algorithm for minimizing the logic function. The combinatorial method of Boolean functions minimization can find practical application in the design of electronic computer systems, because: – minimization of the DNF function is one of the multiextremal logic-combinatorial problems, the solution of which is, in particular, the combinatorial device of the block-diagram with repetition; – extends the capabilities of the algorithm for Boolean functions minimization for their application in information technology; – improves the algebraic method of Boolean function minimization due to the tabular organization of the method, the introduction of the shaped transformation apparatus and the rules of super-sticking of variables.

Opportunistic Device Association for Heterogeneous Cellular Networks With H2H/IoT Co-Existence Under QoS Guarantee

The integration of Internet of Things (IoT) and heterogeneous cellular networks (HCNs) forms a promising paradigm for next generation mobile systems. In this paper, a new association algorithm with quality of service provisioning is proposed to consider the diverse association requirements for human-to-human (H2H) communications and IoT devices (IoTDs) coexisted in HCN. In this context, the devices are categorized into two main classes; rate oriented devices (RODVs) and power oriented devices (PODVs). RODVs are primarily used to model H2H devices while PODVs are mainly used to model IoTDs during the association process. Then, the device association is formulated as an adaptive optimization problem that considers DL rate only, UL transmit power only or both of them according to devices orientations. Since the formulated optimization problem is hard to solve due to the combinatorial device association indicators, we reformulate the proposed optimization problem into a better tractable problem by relaxing the combinatorial indicators. Then, Lagrange dual decomposition method is adopted to find the optimal solution. Moreover, a radio channel distribution mechanism is proposed as a subsequent step to the device association phase for RODVs where the remaining resources after device association phase are distributed among the RODVs. Simulation results show that our proposed algorithm outperforms the comparable schemes especially in terms of power distribution for PODVs and rate distribution for RODVs with a significant rate gain.

The joint embedding property and maximal models

We introduce the notion of a `pure' Abstract Elementary Class to block trivial counterexamples. We study classes of models of bipartite graphs and show: Main Theorem (cf. Theorem 3.34 and Corollary 3.38): If $$\langle \lambda _i: i\le \alpha <\aleph _1\rangle $$??i:i≤?<?1? is a strictly increasing sequence of characterizable cardinals (Definition 2.1) whose models satisfy JEP$$(<\lambda _0)$$(<?0), there is an $$L_{\omega _1,\omega }$$L?1,?-sentence $$\psi $$? whose models form a pure AEC and(1)The models of $$\psi $$? satisfy JEP$$(<\lambda _0)$$(<?0), while JEP fails for all larger cardinals and AP fails in all infinite cardinals.(2)There exist $$2^{\lambda _i^+}$$2?i+ non-isomorphic maximal models of $$\psi $$? in $$\lambda _i^+$$?i+, for all $$i\le \alpha $$i≤?, but no maximal models in any other cardinality; and(3)$$\psi $$? has arbitrarily large models. In particular this shows the Hanf number for JEP and the Hanf number for maximality for pure AEC with Lowenheim number $$\aleph _0$$?0 are at least $$\beth _{\omega _1}$$??1. We show that although $$AP(\kappa )$$AP(?) for each $$\kappa $$? implies the full amalgamation property, $$JEP(\kappa )$$JEP(?) for each $$\kappa $$? does not imply the full joint embedding property. We prove the main combinatorial device of this paper cannot be used to extend the main theorem to a complete sentence.

Fine polar invariants of minimal singularities of surfaces

We consider the polar curves PS,0 arising from generic projections of a germ (S, 0) of complex surface singularity onto C. Taking (S, 0) to be a minimal singularity of normal surface (i.e. a rational singularity with reduced tangent cone), we give the δ-invariant of these polar curves, as well as the equisingularity-type of their generic plane projections, which are also the discriminants of generic projections of (S, 0). These two (equisingularity)-data for PS,0 are described in term, on the one side of the geometry of the tangent cone of (S, 0) and on the other side of the limit-trees introduced by T. de Jong and D. van Straten for the deformation theory of these minimal singularities. These trees give a combinatorial device for the description of the polar curve which makes it much clearer than in our previous Note on the subject. This previous work mainly relied on a result of M. Spivakovsky. Here we give a geometrical proof via deformations (on the tangent cone, and what we call Scott deformations) and blow-ups, although we need Spivakovsky’s result at some point, extracting some other consequences of it along the way.

Multifunctional therapeutic delivery strategies for effective neuro-regeneration following traumatic spinal cord injury.

Traumatic Spinal Cord Injuries (TSCI), due to their devastating nature, present several interventional challenges (extensive inflammation, axonal tethering, scar formation, neuronal degeneration and functional loss) that need to be addressed before even a slight neuronal recovery can be achieved. Recent post-TSCI investigational approaches include a combination of "support and therapeutic" strategies capable of providing localized delivery of therapeutic molecules along with specialized architecture to allow axonal growth and conformal repair. This review provides a brief overview of multifunctional therapeutic delivery strategies for effective neuroregeneration post-TSCI with special emphasis on intrathecal hydrogel-based injectable systems, chondroitinase ABC releasing matrices, micro/nano-sized particulate strategies, 3D-scaffold architectures, biopolymeric channeled bridges for directed neuronal growth, functionalized nerve conduits, nano- and micro-fibrous scaffolds and multicomponent combinatorial paradigms for localized delivery to spinal cord. In addition; a comprehensive account of most widely employed macromolecules and the related neuro-pharmacological, -anatomical, and -functionaloutcomes conferred by the abovementioned neural tissue engineering approaches is provided. Furthermore, the performance of individual delivery systems towards the enhancement of effectiveness, efficiency, and stability of therapeutic molecules and neurotrophic factors is discussed. In conclusion, it is suggested that a multifunctional combinatorial device assimilating the biomaterial, cellular, molecular, structural and functional aspects altogether is the best way forward for effective neuroregeneration post-TSCI.

Peripheral Nerve Regeneration Strategies: Electrically Stimulating Polymer Based Nerve Growth Conduits.

Treatment of large peripheral nerve damages ranges from the use of an autologous nerve graft to a synthetic nerve growth conduit. Biological grafts, in spite of many merits, show several limitations in terms of availability and donor site morbidity, and outcomes are suboptimal due to fascicle mismatch, scarring, and fibrosis. Tissue engineered nerve graft substitutes utilize polymeric conduits in conjunction with cues both chemical and physical, cells alone and or in combination. The chemical and physical cues delivered through polymeric conduits play an important role and drive tissue regeneration. Electrical stimulation (ES) has been applied toward the repair and regeneration of various tissues such as muscle, tendon, nerve, and articular tissue both in laboratory and clinical settings. The underlying mechanisms that regulate cellular activities such as cell adhesion, proliferation, cell migration, protein production, and tissue regeneration following ES is not fully understood. Polymeric constructs that can carry the electrical stimulation along the length of the scaffold have been developed and characterized for possible nerve regeneration applications. We discuss the use of electrically conductive polymers and associated cell interaction, biocompatibility, tissue regeneration, and recent basic research for nerve regeneration. In conclusion, a multifunctional combinatorial device comprised of biomaterial, structural, functional, cellular, and molecular aspects may be the best way forward for effective peripheral nerve regeneration.

A Compact Combinatorial Device for Measurement of Nonlinearity of Radiation Detectors

A new compact computer-controlled device using a combinatorial technique for measuring the nonlinearity of radiation detectors is described. The device consists of two sets of four beam-splitter cubes optically cemented together and arranged so that radiation from a single source is split into four separate paths, then recombined after passing through one of five neutral density filters placed in each path. This allows for the measurement of 625 approximately equi-spaced inter-related flux levels based on only 16 unknown transmittance values. These can be solved for by least-squares fitting, leaving 609 degrees of freedom remaining to determine the nonlinearity of the detector. A novel aspect of the design is the use of neutral density glass plates optically cemented along all the external faces of the beam-splitter cubes, which act as beam dumps for any reflected or scattered radiation. The cube faces in the desired beam paths have clear glass plates with an anti-reflection coating applied at the wavelength of interest optically cemented to them. Operation at other wavelengths is achieved by simply replacing these plates with plates coated for the new wavelength. The performance of the device has been tested using a silicon photodiode with a collimated 650 nm LED as the source. The results demonstrate that the device is able to measure linearity to better than 1 part in \(10^{4}\).

Conformal blocks, Berenstein–Zelevinsky triangles, and group-based models

Work of Buczynska, Wiśniewski, Sturmfels and Xu, and the second author has linked the group-based phylogenetic statistical model associated with the group $$\mathbb {Z}/2\mathbb {Z}$$ Z / 2 Z with the Wess---Zumino---Witten (WZW) model of conformal field theory associated to $$\mathrm {SL}_2(\mathbb {C})$$ SL 2 ( C ) . In this article we explain how this connection can be generalized to establish a relationship between the phylogenetic statistical model for the cyclic group $$\mathbb {Z}/m\mathbb {Z}$$ Z / m Z and the WZW model for the special linear group $$\mathrm {SL}_m(\mathbb {C}).$$ SL m ( C ) . We use this relationship to also show how a combinatorial device from representation theory, the Berenstein---Zelevinsky triangle, corresponds to elements in the affine semigroup algebra of the $$\mathbb {Z}/3\mathbb {Z}$$ Z / 3 Z phylogenetic statistical model.

On a symbolic representation of non-central Wishart random matrices with applications

By using a symbolic method, known in the literature as the classical umbral calculus, the trace of a non-central Wishart random matrix is represented as the convolution of the traces of its central component and of a formal variable matrix. Thanks to this representation, the moments of this random matrix are proved to be a Sheffer polynomial sequence, allowing us to recover several properties. The multivariate symbolic method generalizes the employment of Sheffer representation and a closed form formula for computing joint moments and cumulants (also normalized) is given. By using this closed form formula and a combinatorial device, known in the literature as necklace, an efficient algorithm for their computations is set up. Applications are given to the computation of permanents as well as to the characterization of inherited estimators of cumulants, which turn useful in dealing with minors of non-central Wishart random matrices. An asymptotic approximation of generalized moments involving free probability is proposed.

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

Micromachined nanocalorimetry sensors have shown excellent performance for high-temperature and high-scanning rate calorimetry measurements. Here, we combine scanning AC nanocalorimetry with in-situ x-ray diffraction (XRD) to facilitate interpretation of the calorimetry measurements. Time-resolved XRD during in-situ operation of nanocalorimetry sensors using intense, high-energy synchrotron radiation allows unprecedented characterization of thermal and structural material properties. We demonstrate this experiment with detailed characterization of the melting and solidification of elemental Bi, In, and Sn thin-film samples, using heating and cooling rates up to 300 K/s. Our experiments show that the solidification process is distinctly different for each of the three samples. The experiments are performed using a combinatorial device that contains an array of individually addressable nanocalorimetry sensors. Combined with XRD, this device creates a new platform for high-throughput mapping of the composition dependence of solid-state reactions and phase transformations.

A Model Development for Evaluating Soot-NOx Interactions in a Blended 2-Way Diesel Particulate Filter/Selective Catalytic Reduction

The 2-way diesel particulate filter/selective catalytic reduction (DPF/SCR) emission reduction system has been considered as a potential candidate for future emission standards owing to its advantages in cost savings and packaging flexibility. For the 2-way device, Cu–zeolite is coated inside the DPF substrate as nitrogen oxide (NOx) reducing (DeNOx) catalytic material. Therefore, when exhaust gas passes through the 2-way device, NOx reduction and soot filtration occur simultaneously. However, the operating characteristics of the combinatorial device might be different from individual DPF and SCR devices. In this work, a previously developed model was improved to include soot filtration and oxidation. The model has been tested and validated with experimental data from a reactor flow bench in a systematic manner and applied to capture the effect of soot deposits on NOx reduction performance in a 2-way DPF/SCR device. Accordingly, the soot oxidation characteristics of a 2-way device are investigated with va...

A Prospect for Evolutionary Adequacy: Merge and the Evolution and Development of Human Language

Biolinguistic minimalism seeks a deeper explanation of the design, development and evolution of human language by reducing its core domain to the bare minimum including the set-formation operation Merge. In an attempt to open an avenue of research that may lead to an evolutionarily adequate theory of language, this article makes the following proposals: (i) Merge is the elementary combinatorial device that requires no more decomposition; (ii) the precursor to Merge may be found in the uniquely human capacity for hierarchical object manipulation; (iii) the uniqueness of the human lexicon may also be captured in terms of Merge. Empirical validations of these proposals should constitute one major topic for the biolinguistic program.

Method for segregation of suspected logical malfunctions in combinatorial discrete devices

Consideration was given to the direct problem of technical diagnosis which lies in determining the technical state of a combinatorial discrete device from the results of testing. The graph and analytical models of behavior of the combinatorial discrete device allowing for the technical state of its elements were presented. A method of segregation of the suspected logical malfunctions under which observable behavior of the combinatorial discrete device is possible was proposed.

Optimizing OLED Structures for a-Si Display Applications via Combinatorial Methods and Enhanced Outcoupling

Active-matrix organic light-emitting displays driven by amorphous silicon (a-Si) thin-film transistors (TFT) require superior organic light-emitting device (OLED) performance in order to achieve sufficient pixel brightness and to avoid degradation of the a-Si transistors. In addition, the a-Si TFT circuitry of high-resolution full-color displays can become rather complex and therefore occupies a large amount of the pixel area, leading to a significantly reduced aperture ratio with conventional bottom-emitting OLEDs. A top-emitting device architecture is therefore advantageous. In this paper we describe general concepts for optimizing top-emitting OLEDs via combinatorial methods and for enhancing outcoupling. To optimize OLED performance, we use combinatorial device fabrication. Our system allows the simultaneous fabrication of 10 × 10 individual devices on one substrate, enabling a systematic variation of material combinations and electrodes as well as of device parameters such as layer thickness, layer sequence, and dye dopant concentrations. In the first part, we present an overview of the capabilities of combinatorial methods for electrical and electro-optical device optimization. We show results on multilayer OLEDs ranging from trilayer devices to phosphorescent five-layer OLEDs. The second part describes an outcoupling concept that allows the emission characteristics of top-emitting OLEDs to be tailored. We demonstrated that and analyzed how the angular intensity distribution and the spectral characteristics can be tuned. Light outcoupling can be enhanced by simply varying the optical thickness of a dielectric layer deposited on top of a semitransparent metal electrode. Using this capping-layer concept the outcoupled light intensity in forward direction was increased by a factor of 1.7 while concomittantly achieving a high color purity. The strength of the capping-layer concept is in particular that the optical and the electrical device performance can be optimized separately. Using optimized layer thicknesses and the capping concept, we achieve an efficiency of NTSC (National Television Standard Committee) white from separate red, green and blue sub-pixels exceeding 22 cd/A under realistic display-driving conditions, thus enabling the world's largest (20-inch) a-Si active-matrix OLED display. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)