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Dynamic Pricing and Distributed Energy Management for Demand ResponseJan 11 2016Feb 29 2016The problem of dynamic pricing of electricity in a retail market is considered. A Stackelberg game is used to model interactions between a retailer and its customers; the retailer sets the day-ahead hourly price of electricity and consumers adjust real-time ... More

Impact of Data Quality on Real-Time Locational Marginal PriceDec 29 2012Aug 30 2013The problem of characterizing impacts of data quality on real-time locational marginal price (LMP) is considered. Because the real-time LMP is computed from the estimated network topology and system state, bad data that cause errors in topology processing ... More

Multi-Area Interchange Scheduling under UncertaintyNov 15 2016The problem of multi-area interchange scheduling under system uncertainty is considered. A new scheduling technique is proposed for a multi-proxy bus system based on stochastic optimization that captures uncertainty in renewable generation and stochastic ... More

Distributed Learning and Multiaccess of On-Off ChannelsNov 09 2012Feb 25 2013The problem of distributed access of a set of N on-off channels by K<N users is considered. The channels are slotted and modeled as independent but not necessarily identical alternating renewal processes. Each user decides to either observe or transmit ... More

Capacity of Cooperative Fusion in the Presence of Byzantine SensorsJul 14 2006The problem of cooperative fusion in the presence of Byzantine sensors is considered. An information theoretic formulation is used to characterize the Shannon capacity of sensor fusion. It is shown that when less than half of the sensors are Byzantine, ... More

Estimation after Parameter Selection: Performance Analysis and Estimation MethodsMar 01 2015In many practical parameter estimation problems, prescreening and parameter selection are performed prior to estimation. In this paper, we consider the problem of estimating a preselected unknown deterministic parameter chosen from a parameter set based ... More

Renewables and Storage in Distribution Systems: Centralized vs. Decentralized IntegrationJan 11 2016The problem of integrating renewables and storage into a distribution network is considered under two integration models: (i) a centralized model involving a retail utility that owns the integration as part of its portfolio of energy resources, and (ii) ... More

Distributed Source Coding in the Presence of Byzantine SensorsOct 25 2007The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown group of sensors have been reprogrammed by a malicious intruder to undermine the reconstruction at the fusion center. Three ... More

Variable-Rate Distributed Source Coding in the Presence of Byzantine SensorsMay 07 2007The distributed source coding problem is considered when the sensors, or encoders, are under Byzantine attack; that is, an unknown number of sensors have been reprogrammed by a malicious intruder to undermine the reconstruction at the fusion center. Three ... More

On the Efficiency of Connection Charges---Part I: A Stochastic FrameworkFeb 06 2017This two-part paper addresses the design of retail electricity tariffs for distribution systems with distributed energy resources such as solar power and storage. In particular, the optimal design of dynamic two-part tariffs for a regulated monopolistic ... More

Algorithmic Bidding for Virtual Trading in Electricity MarketsFeb 08 2018We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on the differences between day-ahead and real-time market prices; both prices, however, are random and unknown to ... More

Online Learning and Optimization of Markov Jump Affine ModelsMay 07 2016The problem of online learning and optimization of unknown Markov jump affine models is considered. An online learning policy, referred to as Markovian simultaneous perturbations stochastic approximation (MSPSA), is proposed for two different optimization ... More

Probabilistic Forecast of Real-Time LMP and Network CongestionMar 20 2015Jun 25 2016The short-term forecasting of real-time locational marginal price (LMP) and network congestion is considered from a system operator perspective. A new probabilistic forecasting technique is proposed based on a multiparametric programming formulation that ... More

Detection of Gauss-Markov Random Fields with Nearest-Neighbor DependencyJun 11 2007Jun 08 2010The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) is analyzed. Assuming an acyclic dependency graph, an expression for the log-likelihood ratio of detection is derived. Assuming random placement of nodes over ... More

Sensor Configuration and Activation for Field Detection in Large Sensor ArraysFeb 19 2005The problems of sensor configuration and activation for the detection of correlated random fields using large sensor arrays are considered. Using results that characterize the large-array performance of sensor networks in this application, the detection ... More

Online Learning of Optimal Bidding Strategy in Repeated Multi-Commodity AuctionsMar 07 2017Nov 17 2017We study the online learning problem of a bidder who participates in repeated auctions. With the goal of maximizing his T-period payoff, the bidder determines the optimal allocation of his budget among his bids for $K$ goods at each period. As a bidding ... More

Stochastic Interchange Scheduling in the Real-Time Electricity MarketJan 10 2016The problem of multi-area interchange scheduling in the presence of stochastic generation and load is considered. A new interchange scheduling technique based on a two-stage stochastic minimization of overall expected operating cost is proposed. Because ... More

An online learning approach to dynamic pricing for demand responseApr 04 2014In this paper, the problem of optimal dynamic pricing for retail electricity with an unknown demand model is considered. Under the day-ahead dynamic pricing (a.k.a. real time pricing) mechanism, a retailer obtains electricity in a twosettlement wholesale ... More

Maximum Likelihood Fusion of Stochastic MapsMar 25 2013The fusion of independently obtained stochastic maps by collaborating mobile agents is considered. The proposed approach includes two parts: matching of stochastic maps and maximum likelihood alignment. In particular, an affine invariant hypergraph is ... More

Cognitive Coexistence between Infrastructure and Ad-hoc SystemsDec 07 2008The rapid proliferation of wireless systems makes interference management more and more important. This paper presents a novel cognitive coexistence framework, which enables an infrastructure system to reduce interference to ad-hoc or peer-to-peer communication ... More

Deadline Scheduling as Restless BanditsOct 03 2016The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines.The service provider ... More

Deadline Scheduling as Restless BanditsOct 03 2016Jul 06 2017The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines. The service provider ... More

Market Dynamics and Indirect Network Effects in Electric Vehicle DiffusionFeb 12 2015Jul 06 2015The diffusion of electric vehicles (EVs) is studied in a two-sided market framework consisting of EVs on the one side and EV charging stations (EVCSs) on the other. A sequential game is introduced as a model for the interactions between an EVCS investor ... More

On Robust Tie-line Scheduling in Multi-Area Power SystemsApr 24 2017Oct 06 2017The tie-line scheduling problem in a multi-area power system seeks to optimize tie-line power flows across areas that are independently operated by different system operators (SOs). In this paper, we leverage the theory of multi-parametric linear programming ... More

Generalized Coordinated Transaction Scheduling: A Market Approach to Seamless InterfacesFeb 06 2017Dec 27 2017A generalization of the coordinated transaction scheduling (CTS)---the state-of-the-art interchange scheduling---is proposed. Referred to as generalized coordinated transaction scheduling (GCTS), the proposed approach addresses major seams issues of CTS: ... More

Delay Optimal Multichannel Opportunistic AccessJul 31 2011The problem of minimizing queueing delay of opportunistic access of multiple continuous time Markov channels is considered. A new access policy based on myopic sensing and adaptive transmission (MS-AT) is proposed. Under the framework of risk sensitive ... More

Subspace Methods for Data Attack on State Estimation: A Data Driven ApproachJun 03 2014Data attacks on state estimation modify part of system measurements such that the tempered measurements cause incorrect system state estimates. Attack techniques proposed in the literature often require detailed knowledge of system parameters. Such information ... More

Polytope Codes Against Adversaries in NetworksDec 14 2011Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the network, in that ... More

Optimal and Suboptimal Detection of Gaussian Signals in Noise: Asymptotic Relative EfficiencyJul 06 2005The performance of Bayesian detection of Gaussian signals using noisy observations is investigated via the error exponent for the average error probability. Under unknown signal correlation structure or limited processing capability it is reasonable to ... More

A Large Deviations Approach to Sensor Scheduling for Detection of Correlated Random FieldsJan 21 2005The problem of scheduling sensor transmissions for the detection of correlated random fields using spatially deployed sensors is considered. Using the large deviations principle, a closed-form expression for the error exponent of the miss probability ... More

Algorithmic Bidding for Virtual Trading in Electricity MarketsFeb 08 2018Jul 31 2018We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on the differences between day-ahead and real-time market prices; both prices, however, are random and unknown to ... More

Anonymous Networking amidst EavesdroppersOct 25 2007The problem of security against timing based traffic analysis in wireless networks is considered in this work. An analytical measure of anonymity in eavesdropped networks is proposed using the information theoretic concept of equivocation. For a physical ... More

Large-scale Charging of Electric Vehicles: A Multi-Armed Bandit ApproachMay 24 2016The successful launch of electric vehicles (EVs) depends critically on the availability of convenient and economic charging facilities. The problem of scheduling of large-scale charging of EVs by a service provider is considered. A Markov decision process ... More

Probabilistic Forecasting and Simulation of Electricity Markets via Online Dictionary LearningJun 25 2016The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based ... More

Dynamic Scheduling for Charging Electric Vehicles: A Priority RuleFeb 01 2016We consider the scheduling of multiple tasks with pre-determined deadlines under random processing cost. This problem is motivated by the potential of large scale adoption of plug-in (hybrid) electric vehicles (PHEVs) in the near future. The charging ... More

Data Framing Attack on State EstimationOct 28 2013Apr 21 2014A new mechanism aimed at misleading a power system control center about the source of a data attack is proposed. As a man-in-the-middle state attack, a data framing attack is proposed to exploit the bad data detection and identification mechanisms currently ... More

Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and PropertiesJun 08 2005Jan 04 2006The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the state-space structure of the signal and observation model, ... More

Optimal Deadline Scheduling with CommitmentOct 06 2011We consider an online preemptive scheduling problem where jobs with deadlines arrive sporadically. A commitment requirement is imposed such that the scheduler has to either accept or decline a job immediately upon arrival. The scheduler's decision to ... More

On the Dynamics of Distributed Energy Adoption: Equilibrium, Stability, and Limiting CapacityMar 20 2018Oct 16 2018The death spiral hypothesis in electric utility represents a positive feedback phenomenon in which a regulated utility is driven to financial instability by rising prices and declining demand. We establish conditions for the existence of death spiral ... More

No-Core Monte Carlo Shell Model Calculations with Unitary Correlation Operator Method and Similarity Renormalization GroupNov 22 2014The unitary correlation operator method (UCOM) and the similarity renormalization group theory (SRG) are compared and discussed in the framework of no-core Monte Carlo shell model (MCSM) calculations for $^{3}$H and $^{4}$He. The treatment of spurious ... More

The field Q(2cos(pi/n)), its Galois group and length ratios in the regular n-gonOct 03 2012The normal field extension Q(rho(n)), with the algebraic number rho(n) = 2 cos(pi/n) for natural n, is related to ratios of the lengths between diagonals and the side of a regular n-gon. This has been considered in a paper by P. Steinbach. These ratios ... More

Reduce and Solve Boltzmann Equation on a Global Lie GroupDec 13 2010Aug 11 2011This paper has been withdrawn by the author due to a crucial sign error in equation 2.23 and a wrong author added.

On the image of the Galois representation associated to a non-CM Hida familySep 30 2014Fix a prime $p > 2$. Let $\rho : \text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \to \text{GL}_2(\mathbb{I})$ be the Galois representation coming from a non-CM irreducible component $\mathbb{I}$ of Hida's $p$-ordinary Hecke algebra. Assume the residual representation ... More

The Tribonacci and ABC Representations of Numbers are EquivalentOct 23 2018It is shown that the unique representation of positive integers in terms of tribonacci numbers and the unique representation in terms of iterated A, B and C sequences defined from the tribonacci word are equivalent. These sequences are studied in detail. ... More

Regularization methods for finding the relaxation time spectra of linear polydisperse polymer meltsFeb 19 2018The calculation of discrete or continuous relaxation time spectra from rheometric measurables of polydisperse polymers is an ill-posed problem. In this paper, a curve fitting method for solving this problem is presented and compared to selected models ... More

Knowledge reduction of dynamic covering decision information systems with immigration of more objectsApr 01 2015In practical situations, it is of interest to investigate computing approximations of sets as an important step of knowledge reduction of dynamic covering decision information systems. In this paper, we present incremental approaches to computing the ... More

Decision-theoretic rough sets-based three-way approximations of interval-valued fuzzy setsDec 22 2014In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds ... More

Three-Way Decisions-Based Conflict Analysis ModelsMar 07 2019Three-way decision theory, which trisects the universe with less risks or costs, is considered as a powerful mathematical tool for handling uncertainty in incomplete and imprecise information tables, and provides an effective tool for conflict analysis ... More

Correlations in low-dimensional quantum gasesDec 14 2017Ultracold gases are a versatile platform to simulate condensed matter physics, as virtually any parameter is experimentally tunable. In particular, highly anisotropic traps allow the realization of low-dimensional systems, where the role of quantum fluctuations ... More

Related family-based attribute reduction of covering information systems when varying attribute setsNov 16 2017In practical situations, there are many dynamic covering information systems with variations of attributes, but there are few studies on related family-based attribute reduction of dynamic covering information systems. In this paper, we first investigate ... More

A Subspace Technique for The Identification of Switched Affine ModelsSep 13 2013The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is estimated from observations. ... More

Spectral Clustering on Subspace for Parameter Estimation of Jump Linear ModelsJul 01 2013The problem of estimating parameters of a deterministic jump or piecewise linear model is considered. A subspace technique referred to as spectral clustering on subspace (SCS) algorithm is proposed to estimate a set of linear model parameters, the model ... More

PMU based Detection of Imbalance in Three-Phase Power SystemsSep 19 2014The problem of imbalance detection in a three-phase power system using a phasor measurement unit (PMU) is considered. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is presented and a hypothesis ... More

Coordinated Multi-area Economic Dispatch via Critical Region ProjectionJun 13 2016A coordinated economic dispatch method for multi-area power systems is proposed. Choosing boundary phase angles as coupling variables, the proposed method exploits the structure of critical regions in local problems defined by active and inactive constraints. ... More

On the Efficiency of Connection Charges---Part II: Integration of Distributed Energy ResourcesFeb 06 2017This two-part paper addresses the design of retail electricity tariffs for distribution systems with distributed energy resources (DERs). Part I presents a framework to optimize an ex-ante two-part tariff for a regulated monopolistic retailer who faces ... More

The Inverse of a Nearly Banded MatrixNov 30 2008A quantitative form of the Nullity Theorem is presented, which establishes a linear relation between the singular values of the two submatrices involved in the theorem up to the first order. The theorem is then extended to function spaces and a corresponding ... More

A Classification of the Supercharacter Theories of $C_p \times C_2 \times C_2$ for Prime $p$Sep 22 2016We classify and construct all supercharacter theories for the groups $C_p \times C_2 \times C_2$ where $p$ is an odd prime. It is known that every nontrivial supercharacter theory of a cyclic group can be constructed as a wedge product, a direct product, ... More

A Laplace Transform Method for Molecular Mass Distribution Calculation from Rheometric DataFeb 19 2018Polydisperse linear polymer melts can be microscopically described by the tube model and fractal reptation dynamics, while on the macroscopic side the generalized Maxwell model is capable of correctly displaying most of the rheological behavior. In this ... More

Double-quantitative $γ^{\ast}-$fuzzy coverings approximation operatorsNov 24 2016In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak's model is becoming a hot research ... More

Incremental approaches to knowledge reduction of covering decision information systems with variations of coveringsDec 09 2015In practical situations, calculating approximations of concepts is the central step for knowledge reduction of dynamic covering decision information system, which has received growing interests of researchers in recent years. In this paper, the second ... More

Decision-theoretic rough sets based on time-dependent loss functionMar 17 2015A fundamental notion of decision-theoretic rough sets is the concept of loss functions, which provides a powerful tool of calculating a pair of thresholds for making a decision with a minimum cost. In this paper, time-dependent loss functions which are ... More

On Generating functions of Diagonals Sequences of Sheffer and Riordan Number TrianglesAug 04 2017The exponential generating function of ordinary generating functions of diagonal sequences of general Sheffer triangles is computed by an application of Lagrange's theorem. For the special Jabotinsky type this is already known. An analogous computation ... More

Bayesian State Estimation for Unobservable Distribution Systems via Deep LearningNov 07 2018Dec 17 2018The problem of state estimation for unobservable distribution systems is considered. A Bayesian approach is proposed that combines Bayesian inference with deep neural networks to achieve the minimum mean squared error estimation of network states for ... More

Energy Scaling Laws for Distributed Inference in Random Fusion NetworksSep 03 2008Jun 08 2010The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Among the ... More

Bayesian State Estimation for Unobservable Distribution Systems via Deep LearningNov 07 2018Feb 25 2019The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power ... More

The Embedding Capacity of Information Flows Under Renewal TrafficMar 12 2011Mar 15 2011Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching rule is that of ... More

NS5-Branes, T-Duality and Worldsheet InstantonsApr 23 2002Jun 30 2003The equivalence of NS5-branes and ALF spaces under T-duality is well known. However, a naive application of T-duality transforms the ALF space into a smeared NS5-brane, de-localized on the dual, transverse, circle. In this paper we re-examine this duality, ... More

Monopoles in the Higgs PhaseJul 31 2003Aug 14 2003We describe new solutions of Yang-Mills-Higgs theories consisting of magnetic monopoles in a phase with fully broken gauge symmetry. Rather than spreading out radially, the magnetic field lines form flux tubes. The solution is topologically stable and, ... More

Etude locale des torseurs sous une courbe elliptiqueMay 04 2010This article concerns the geometry of torsors under an elliptic curve. Let $\OO_K$ be a complete discrete valuation ring with algebraically closed residue field and function field $K$. Let $\pi$ be a generator of the maximal ideal of $\OO_K$, and $S=\mathrm{Spec}(\OO_K)$. ... More

Some sharp performance bounds for least squares regression with $L_1$ regularizationAug 20 2009We derive sharp performance bounds for least squares regression with $L_1$ regularization from parameter estimation accuracy and feature selection quality perspectives. The main result proved for $L_1$ regularization extends a similar result in [Ann. ... More

Three-Dimensional Gauge Theories and ADE MonopolesMar 18 1998We study three-dimensional N=4 gauge theories with product gauge groups constructed from ADE Dynkin diagrams. One-loop corrections to the metric on the Coulomb branch are shown to coincide with the metric on the moduli space of well-seperated ADE monopoles. ... More

Line Operators in the Standard ModelMay 04 2017Jun 12 2017There is an ambiguity in the gauge group of the Standard Model. The group is $G = SU(3) \times SU(2) \times U(1)/\Gamma$, where $\Gamma$ is a subgroup of ${\bf Z}_6$ which cannot be determined by current experiments. We describe how the electric, magnetic ... More

Simplified dark matter models in the light of AMS-02 antiproton dataDec 30 2016In this work we perform an analysis of the recent AMS-02 antiproton flux and the antiproton-to-proton ratio in the framework of simplified dark matter models. To predict the AMS-02 observables we adopt the propagation and injection parameters determined ... More

Type II Seesaw and tau lepton at the HL-LHC, HE-LHC and FCC-hhFeb 03 2018The tau lepton plays important role in distinguishing neutrino mass patterns and determining the chirality nature in heavy scalar mediated neutrino mass models, in the light of the neutrino oscillation experiments and its polarization measurement. We ... More

Separation of dissipation from diffusionAug 20 2001We study velocity correlations induced by diffusion and dissipation in a simple dissipative dynamical system. We observe that diffusion, as a result of time reversible microscopic processes, leads to correlations with different spatial parity from those ... More

Regularity/Controllability/Observability of an NDS with Descriptor Form Subsystems and Generalized LFTsMar 13 2019This paper investigates regularity, controllability and observability for a networked dynamic system (NDS) with its subsystems being described in a descriptor form and system matrices of each subsystem being represented by a generalized linear fractional ... More

Minimal Inputs/Outputs for a Networked SystemOct 01 2016Mar 18 2017This paper investigates the minimal number of inputs/outputs required to guarantees the controllability/observability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this minimal number is ... More

Slope inequality for families of curves over surfacesDec 12 2015Jun 05 2016In this paper, we investigate the general notion of the slope for families of curves $f: X \to Y$. The main result is an answer to the above question when $\dim Y = 2$, and we prove a lower bound for this new slope in this case over fields of any characteristic. ... More

Minimal Control Selection for a Networked SystemOct 01 2016This paper investigates the minimal number of actuators required to guarantees the controllability of a system, under the condition that its state transition matrix (STM) is prescribed. It has been proved that this minimal number is equal to the maximum ... More

D-Branes in Field TheoryDec 15 2005Jan 04 2006Certain gauge theories in four dimensions are known to admit semi-classical D-brane solitons. These are domain walls on which vortex flux tubes may end. The purpose of this paper is to develop an open-string description of these D-branes. The dynamics ... More

TASI Lectures on SolitonsSep 28 2005Dec 19 2005These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton. We start with instantons and ... More

Lectures on String TheoryAug 03 2009Feb 23 2012This is a one semester course on bosonic string theory aimed at beginning graduate students. The lectures assume a working knowledge of quantum field theory and general relativity. Contents: 1. The Classical String 2. The Quantum String 3. Open Strings ... More

Compatibility of Kisin modules for different uniformizersFeb 07 2013Let p be a prime and T a lattice inside a semi-stable representation V. We prove that Kisin modules associated to T by selecting different uniformizers are isomorphic after tensoring a subring in W(R). As consequences, we show that several lattices inside ... More

Gaining Free or Low-Cost Transparency with Interpretable Partial SubstituteFeb 12 2018May 10 2019This work addresses the situation where a black-box model with good predictive performance is chosen over its interpretable competitors, and we show interpretability is still achievable in this case. Our solution is to find an interpretable substitute ... More

A note on lattices in semi-stable representationsSep 28 2007Let p>2 be a prime, K a finite extension over Q_p and G :=Gal(\bar K/K). We extend Kisin's theory on \phi-modules of finite E(u)-height to give a new classification of G-stable Z_p-lattices in semi-stable representations

Potentially Good Reduction of Barsotti-Tate GroupsApr 27 2006Let R be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field, K the fraction field of R. Suppose G is a Barsotti-Tate group (p-divisible group) defined over K which acquires good reduction over a finite extension ... More

Geography of irregular Gorenstein 3-foldsSep 24 2013Nov 24 2013In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo inequalities for irregular surfaces to irregular 3-folds according to the Albanese dimension. ... More

Robust Recursive State Estimation with Random Measurements DroppingsJan 16 2014A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent observations, ... More

Necessity of numerical smoothnessJul 12 2012Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial smoothness indicators ... More

On the Equivalence among Three Controllability Problems for a Networked SystemOct 11 2016A new proof is given for the mathematical equivalence among three $k$-sparse controllability problems of a networked system, which plays key roles in Olshevsky,2014, in the establishment of the NP-hardness of the associated minimal controllability problems ... More

Minimal Inputs/Outputs for Subsystems in a Networked SystemOct 07 2016Apr 13 2018Minimal input/output selection is investigated in this paper for each subsystem of a networked system. Some novel sufficient conditions are derived respectively for the controllability and observability of a networked system, as well as some necessary ... More

Large polar caps for twisted magnetosphere of rotating magnetarsMay 09 2019The magnetic field of magnetars may be twisted compared with that of normal pulsars. Previous works mainly discussed magnetic energy release in the closed field line regions of magnetars. For a twisted magnetic field, the field lines will inflate in the ... More

Fibonacci numbers and Trivalent graphsJun 19 2013We study the Fibonacci and Lucas numbers and demonstrate how identities can be constructed by investigating trivalent graphs and splitting fields.

Fibonacci Numbers and Identities IIApr 11 2013May 08 2013We give alternative proof of Melham's and Howard's identities on generalised Fibonacci numbers

The index formula for the Hecke group H_5Jan 04 2014May 24 2014The present article gives the index formula of the principal congruence subgroups of the Hecke group H_5

Wohlfahrt's Theorem for the Hecke group G_5Jan 04 2014Let K be a subgroup of the inhomogeneous Hecke group G_5 of finite index. Suppose that the geometric level of K is r. Then K is congruence if and only if K contains the principal congruence subgroup of level 2r.

Recurrence for powers of recursive sequence IIMay 09 2013May 11 2013Let x(n) be a recurrence relation. The main purpose of this article is to determine a recurrence for powers of x(n).

Identifying normal and congruence subgroupsJan 05 2015We give a simple algorithm that enables us to determine whether a subgroup of finite index of the Hecke group is normal.

Fibonacci system and residue completenessApr 10 2013Jul 11 2013We give necessary and sufficient conditions for a Fibonacci cycle to be residue complete (nondefective). In particular, the Lucas numbers modulo m is residue complete if and only if m = 2,4,6,7,14 or a power of 3.

Arithmetic and geometry of the Hecke groupsSep 16 2015We study the arithmetic and geometry properties of the Hecke group $G_q$. In particular, we prove that $G_q$ has a subgroup $X $ of index $d$, genus $g$ with $v_{\infty} $ cusps, and $\tau_2$ (resp. $v_{r_i}$) conjugacy classes of elements that are conjugates ... More