Two-channel Case Research Articles

Shuffled multi-channel sparse signal recovery

Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To address this issue systematically, we frame it as a signal reconstruction problem where correspondences between samples and channels are lost. Assuming a sensing matrix for the signals, we show the problem’s equivalence to a highly structured unlabeled sensing problem and establish conditions for unique recovery. This is crucial since existing unlabeled sensing theory is inapplicable and results for reconstructing shuffled multi-channel signals do not yet exist. Our results extend to continuous-time sparse signals, and we derive conditions for reconstructing shuffled sparse signals. For the two-channel case, we provide a first reconstruction method, which combines sparse signal recovery with robust linear regression, outperforming existing unlabeled sensing methods in numerical experiments. Additionally, we showcase its effectiveness in a real-world application involving calcium imaging traces. Our theory marks a significant initial step in addressing this challenging signal reconstruction problem, with potential extensions to diverse signal representations encountered in real-world problems with imprecise measurement or channel assignment.

The scalar exotic resonances X(3915), X(3960), X_0(4140)

The scalar resonances X(3915), X(3960), X_0(4140) are considered as exotic four-quark states: cqbar{c} bar{q}, csbar{c} bar{s}, csbar{c}bar{s}, while the X(3863) is proved to be the cbar{c}, 2,^3P_0 state. The masses and the widths of these resonances are calculated in the framework of the Extended Recoupling Model, where a four-quark system is formed inside the bag and has relatively small size (lesssim 1.0 fm). Then the resonance X(3915) appears due to the transitions: J/psi omega into D^{*+}D^{*-} (or D^{*0}bar{D}^{*0}) and back, while the X(3960) is created due to the transitions D_s^+D_s^- into J/psi phi and back, and the X_0(4140) is formed in the transitions J/psi phi into D_s^{*+}D_s^{*-} and back. The characteristic feature of the recoupling mechanism is that this type of resonances can be predominantly in the S-wave decay channels and has J^P=0^+. In two-channel case the resonance occurs to be just near the lower threshold, while due to coupling to third channel (like the cbar{c} channel) it is shifted up and lies by (20–30) MeV above the lower threshold. The following masses and widths are calculated: M(X(3915))=3920 MeV, Gamma (X(3915))=20 MeV; M(X(3960))=3970 MeV, Gamma (X(3960)=45(5) MeV, M(X_0(4140))= 4120(20) MeV, Gamma (X_0(4140))=100 MeV, which are in good agreement with experiment.

Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the interimpurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

QFT, EFT and GFT

We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem.

Effective Floquet model for minimally twisted bilayer graphene

We construct an effective Floquet lattice model for the triangular network that emerges in interlayer-biased minimally twisted bilayer graphene and which supports two chiral channels per link for a given valley and spin. We introduce the Floquet scheme with the one-channel triangular network and subsequently extend it to the two-channel case. From the bulk topological index (winding number) and finite system calculations, we find that both cases host anomalous Floquet insulators (AFIs) with a different gap-opening mechanism. In the one-channel network, either time-reversal or in-plane inversion symmetry has to be broken to open a gap. In contrast, in the two-channel network, interchannel coupling can open a gap without breaking these symmetries yielding a valley AFI with counterpropagating edge states. This phase is topologically trivial with respect to the total winding number but robust in the absence of intervalley scattering. Finally, we demonstrate the applicability of the Floquet model with magnetotransport calculations.

Sending classical information via three noisy channels in superposition of causal orders

In this work, we study the transmission of classical information through three completely depolarizing channels in superposition of different causal orders. We thus introduce the quantum 3-switch as a resource for quantum communications. We perform a new kind of quantum control that was not accessible to the previously treated two-channel case. The fine and full quantum control achieved using selected combinations of causal orders let us uncover new features: non monotonous behavior on the transmission of information with respect to the number of causal orders involved, and different values of the transmission of information depending on the specific combinations of causal orders considered. Our results are a stepping stone to assess efficiency of coherent quantum control and optimize resources in the implementation of new indefinite causal structures. Finally, we suggest an optical implementation using standard telecom technology to test our predictions.

Communication Enhancement through Quantum Coherent Control of N Channels in an Indefinite Causal-Order Scenario

In quantum Shannon theory, transmission of information is enhanced by quantum features. Up to very recently, the trajectories of transmission remained fully classical. Recently, a new paradigm was proposed by playing quantum tricks on two completely depolarizing quantum channels i.e., using coherent control in space or time of the two quantum channels. We extend here this control to the transmission of information through a network of an arbitrary number N of channels with arbitrary individual capacity i.e., information preservation characteristics in the case of indefinite causal order. We propose a formalism to assess information transmission in the most general case of N channels in an indefinite causal order scenario yielding the output of such transmission. Then, we explicitly derive the quantum switch output and the associated Holevo limit of the information transmission for , as a function of all involved parameters. We find in the case that the transmission of information for three channels is twice that of transmission of the two-channel case when a full superposition of all possible causal orders is used.

Critical points in two-channel quantum systems

Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wavefunctions. Realistic quantum systems are coupled however mostly to more than one continuum. For example, the conductance of an open cavity needs at least two environments, namely the input and the output channel. In the present paper, we study generic features of the transfer of particles through an open quantum system coupled to two channels. We compare the results with those characteristic of a one-channel system. Of special interest is the parameter range which is influenced by singular points. Here, the states of the system are mixed via the environment. In the one-channel case, the resonance structure of the cross section is independent of the existence of singular points. In the two-channel case, however, new effects appear such as coherence. An example is the enhanced conductance of an open cavity in a certain finite parameter range. It is anti-correlated with the averaged phase rigidity of the eigenfunctions of the non-Hermitian Hamilton operator.Graphical abstract

One- and two-channel Kondo model with logarithmic Van Hove singularity: A numerical renormalization group solution

Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the s–d coupling J. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.

An Opportunistic Sensor Scheduling Solution to Remote State Estimation Over Multiple Channels

We consider a sensor scheduling problem where the sensors have multiple choices of communication channel to send their local measurements to a remote state estimator for state estimation. Specifically, the sensors can transmit high-precision data packets over an expensive channel or low-precision data packets, which are quantized in several bits, over some cheap channels. The expensive channel, though being able to deliver more accurate data which leads to good estimation quality at the remote estimator, can only be used scarcely due to its high cost (e.g., high energy consumption). On the other hand, the cheap channel, though having a small cost, delivers less accurate data which inevitably deteriorates the remote estimation quality. In this work we propose a new framework in which the sensors switch between the two channels to achieve a better tradeoff among the communication cost, the estimation performance and the computational complexity, where the two-channel case can be easily extended to a multiple-channel case. We propose an opportunistic sensor schedule which reduces the communication cost by randomly switching among the expensive and cheap channels, and in the meantime maintains low computational complexity while introducing data quantization into the estimation problem. We present a minimum mean square error (MMSE) estimator in a closed-form under the proposed opportunistic sensor schedule. We also formulate an optimization problem to search the best opportunistic schedule with a linear quantizer. Furthermore, we show that the MMSE estimator in the limiting case becomes the standard Kalman filter.

Forcing Scale Invariance in Multipolarization SAR Change Detection

This paper considers the problem of coherent (in the sense that both amplitudes and relative phases of the polarimetric returns are used to construct the decision statistic) multipolarization synthetic aperture radar change detection starting from the availability of image pairs exhibiting possible power mismatches/miscalibrations. The principle of invariance is used to characterize the class of scale-invariant decision rules which are insensitive to power mismatches and ensure the constant false alarm rate property. A maximal invariant statistic is derived together with the induced maximal invariant in the parameter space which significantly compresses the data/parameter domain. A generalized likelihood ratio test is synthesized both for the cases of two- and three-polarimetric channels. Interestingly, for the two-channel case, it is based on the comparison of the condition number of a data-dependent matrix with a suitable threshold. Some additional invariant decision rules are also proposed. The performance of the considered scale-invariant structures is compared to those from two noninvariant counterparts using both simulated and real radar data. The results highlight the robustness of the proposed method and the performance tradeoff involved.

A Chinese restaurant game for learning and decision making in cognitive radio networks

In cognitive radio networks, secondary users (SUs) are allowed to opportunistically exploit the licensed channels. Once finding the spectrum holes, SUs need to share the available licensed channels. Therefore, one of the critical challenges for fully utilizing the spectrum resources is how the SUs obtain accurate information about the primary users’ (PUs’) activities and make right decisions on which channels to access so as to avoid competition from other SUs. In this paper, we formulate SUs’ learning and decision making process as a Chinese restaurant game, which is concerned with negative network externality, by considering the scenario where each SU senses only one of the channels and then makes access decisions sequentially. In the proposed game, SUs build the knowledge of the PUs’ activities by their own sensing and learning the information from other SUs. They also predict the subsequent SUs’ decisions to maximize their own utilities. We analyze the interactions among SUs and study specifically the impact of SUs’ initial belief, sensing accuracy and channel quality on their decisions. We also derive the theoretical results for the two-user two-channel case and extend the results to the multi-user multi-channel case. Finally, we verify the theoretical results and evaluate the performance of the proposed scheme in terms of social welfare through simulations.

Adaptive reconfigurable V-BLAST type equalizer for cognitive MIMO-OFDM radios

An adaptive channel shortening equalizer design for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) radio receivers is considered in this presentation. The proposed receiver has desirable features for cognitive and software defined radio implementations. It consists of two sections: MIMO decision feedback equalizer (MIMO-DFE) and adaptive multiple Viterbi detection. In MIMO-DFE section, a complete modified Gram-Schmidt orthogonalization of multichannel input data is accomplished using sequential processing multichannel Givens lattice stages, so that a Vertical Bell Laboratories Layered Space Time (V-BLAST) type MIMO-DFE is realized at the front-end section of the channel shortening equalizer. Matrix operations, a major bottleneck for receiver operations, are accordingly avoided, and only scalar operations are used. A highly modular and regular radio receiver architecture that has a suitable structure for digital signal processing (DSP) chip and field programable gate array (FPGA) implementations, which are important for software defined radio realizations, is achieved. The MIMO-DFE section of the proposed receiver can also be reconfigured for spectrum sensing and positioning functions, which are important tasks for cognitive radio applications. In connection with adaptive multiple Viterbi detection section, a systolic array implementation for each channel is performed so that a receiver architecture with high computational concurrency is attained. The total computational complexity is given in terms of equalizer and desired response filter lengths, alphabet size, and number of antennas. The performance of the proposed receiver is presented for two-channel case by means of mean squared error (MSE) and probability of error evaluations, which are conducted for time-invariant and time-variant channel conditions, orthogonal and nonorthogonal transmissions, and two different modulation schemes.

Multiple description discrete cosine transform-based image coding using DC coefficient relocation and AC coefficient interpolation

The development of an effective and dependable multiple description coding scheme over a lossy communication system is described. A general framework of an effective multiple description robust communication system with two-channel and four-channel cases is presented with a proposed block-based DC coefficient relo- cation and AC coefficient interpolation approach. A benefit of such system is that, if all the channels work properly, a very good quality, probably lossless, reconstruction can be obtained from the received descriptions. On the other hand, if some of the channels do not work properly, a lower but still quite satisfactory quality of reconstruction can be obtained. The performance of the proposed scheme is mea- sured with mean squared error, peak signal-to-noise ratio, entropy, and bit rate to analyze the reconstruction quality, and the computed results are matched with that of the other schemes. The system complexity is also computed and compared. Comparing the simula- tion results, it is observed that the proposed scheme, which uses a DC coefficient relocation and AC coefficient interpolation scheme, gives comprehensive enhancements over the other recently devel- oped schemes. © 2013 SPIE and IS&T (DOI: 10.1117/1.JEI.22.2 .023030)

Multichannel dynamical symmetry and cluster-coexistence

A composite symmetry of the nuclear structure, called multichannel dynamical symmetry is established. It can describe different cluster configurations (defined by different reaction channels) in a unified framework, thus it has a considerable predictive power. The two-channel case is presented in detail, and its conceptual similarity to the dynamical supersymmetry is discussed.

Strongly correlated dynamics in multichannel quantum RC circuits

We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or single-electron box capacitively coupled to a gate and connected to a reservoir lead via several conducting channels. Depending on the engineering details of the quantum RC circuit, the number of channels contributing to transport vary, as do the form of the interchannel couplings. For low-frequency AC transport, the charge-relaxation resistance ($R_{q}$) is a nontrivial function of the parameters of the system. However, in the vicinity of the charge degeneracy points and for weak tunneling, we find as a result of cross-mode mixing or channel asymmetry that $R_q$ becomes universal for a metallic cavity at low temperatures, and equals the unit of quantum resistance. To prove this universality we map the system to an effective one-channel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of near-perfect transmission using a bosonization approach. Focussing on the two-channel case, we study the effect of backscattering at the lead-dot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weak tunneling regime near the charge degeneracy points.

Theory of deuteron stripping: From surface integrals to a generalizedR-matrix approach

There are two main reasons for the absence of a practical theory of stripping to resonance states that could be used by experimental groups: The numerical problem of the convergence of the distorted-wave Born approximation (DWBA) matrix element when the full transition operator is included and the ambiguity over what spectroscopic information can be extracted from the analysis of transfer reactions populating the resonance states. The purpose of this paper is to address both questions. The theory of the deuteron stripping is developed, which is based on the post continuum discretized coupled channels (CDCCs) formalism going beyond of the DWBA and surface integral formulation of the reaction theory [A. S. Kadyrov et al., Ann. Phys. 324, 1516 (2009)]. First, the formalism is developed for the DWBA and then it is extended to the CDCC formalism, which is the ultimate goal of this work. The CDCC wave function takes into account not only the initial elastic $d+A$ channel but also its coupling to the deuteron breakup channel $p+n+A$ missing in the DWBA. Stripping to both bound states and resonances is included. The convergence problem for stripping to resonance states is solved in the post CDCC formalism. The reaction amplitude is parametrized in terms of the reduced width amplitudes (asymptotic normalization coefficients), inverse level matrix, boundary condition, and channel radius, which are the same parameters used in the conventional $R$-matrix method. For stripping to resonance states, many-level and one- and two-channel cases are considered. The theory provides a consistent tool to analyze both binary resonant reactions and deuteron stripping in terms of the same parameters.

On myopic sensing for multi-channel opportunistic access: structure, optimality, and performance

We consider a multi-channel opportunistic communication system where the states of these channels evolve as independent and statistically identical Markov chains (the Gilbert-Elliot channel model). A user chooses one channel to sense and access in each slot and collects a reward determined by the state of the chosen channel. The problem is to design a sensing policy for channel selection to maximize the average reward, which can be formulated as a multi-arm restless bandit process. In this paper, we study the structure, optimality, and performance of the myopic sensing policy. We show that the myopic sensing policy has a simple robust structure that reduces channel selection to a round-robin procedure and obviates the need for knowing the channel transition probabilities. The optimality of this simple policy is established for the two-channel case and conjectured for the general case based on numerical results. The performance of the myopic sensing policy is analyzed, which, based on the optimality of myopic sensing, characterizes the maximum throughput of a multi-channel opportunistic communication system and its scaling behavior with respect to the number of channels. These results apply to cognitive radio networks, opportunistic transmission in fading environments, and resource-constrained jamming and anti-jamming.

Matrix Filters for the Detection of Extragalactic Point Sources in Cosmic Microwave Background Images

In this paper we introduce a new linear filtering technique, the so-called matrix filters, that maximizes the signal-to-interference ratio of compact sources of unknown intensity embedded in a set of images by taking into account the cross-correlations between the different channels. By construction, the new filtering technique outperforms (or at least equals) the standard matched filter applied on individual images. An immediate application is the detection of extragalactic point sources in cosmic microwave background images obtained at different wavelengths. We test the new technique in two simulated cases: a simple two-channel case with ideal correlated color noise and more realistic simulations of the sky as it will be observed by the low-frequency instrument instrument of the upcoming ESA's Planck mission. In both cases, we observe an improvement with respect to the standard matched filter in terms of signal-to-noise interference, number of detections and number of false alarms.

Kondo lattice model at half-filling

In this paper, we have studied the single- and two-channel Kondo lattice modelconsisting of localized spins interacting anti-ferromagnetically with itinerant electrons.We have employed the dynamical mean field theory and have used the exactdiagonalization method in our impurity solver. This method allowed us to accesslow temperatures and large values of exchange couplings. Our results for thesingle-channel case confirm and extend the recent investigations. In the two-channelcase, at absolute zero temperature for half-filling and for the exchange couplingsJ/t>0.8, we have found a spontaneous symmetry breaking quantum phase transition, with oneband showing a metallic behavior and the other showing an insulating behavior. Finally,our calculations for the two-channel case show the existence of an anti-ferromagnetic phasefor all coupling strengths of physical interest.