arXiv subjects

Cong Shi

Publications and source records attributed to Cong Shi.

41 records · Page 3Linked to original sources

arXiv2016

Singular Values of the Attenuated Photoacoustic Imaging Operator

We analyse the ill-posedness of the photoacoustic imaging problem in the case of an attenuating medium. To this end, we introduce an attenuated photoacoustic operator and determine the asymptotic behaviour of its singular values. Dividing the known attenuation models into strong and weak attenuation classes, we show that for strong attenuation, the singular values of the attenuated photoacoustic operator decay exponentially, and in the weak attenuation case the singular values of the attenuated photoacoustic operator decay with the same rate as the singular values of the non-attenuated photoacoustic operator.

math.FA↗

arXiv2016

A signal separation technique for sub-cellular imaging using dynamic optical coherence tomography

This paper aims at imaging the dynamics of metabolic activity of cells. Using dynamic optical coherence tomography, we introduce a new multi-particle dynamical model to simulate the movements of the collagen and the cell metabolic activity and develop an efficient signal separation technique for sub-cellular imaging. We perform a singular-value decomposition of the dynamic optical images to isolate the intensity of the metabolic activity. We prove that the largest eigenvalue of the associated Casorati matrix corresponds to the collagen. We present several numerical simulations to illustrate and validate our approach.

math.NA↗

arXiv2015

Dynamic Allocation Problems in Loss Network Systems with Advanced Reservation

We consider a class of well-known dynamic resource allocation models in loss network systems with advanced reservation. The most important performance measure in any loss network system is to compute its blocking probability, i.e., the probability of an arriving customer in equilibrium finds a fully utilized system (thereby getting rejected by the system). In this paper, we derive upper bounds on the asymptotic blocking probabilities for such systems in high-volume regimes. There have been relatively few results on loss network systems with advanced reservation due to its inherent complexity. The theoretical results find applications in a wide class of revenue management problems in systems with reusable resources and advanced reservation, e.g., hotel room, car rental and workforce management. We propose a simple control policy called the improved class selection policy (ICSP) based on solving a continuous knapsack problem, similar in spirit to the one proposed in Levi and Radovanovic (2010). Using our results derived for loss network systems with advanced reservation, we show the ICSP performs asymptotically near-optimal in high-volume regimes.

math.PR↗

arXiv2015

Approximation Algorithms for Inventory Problems with Submodular or Routing Costs

We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer who faces demands. In each time step, any subset of item-types can be ordered incurring a joint ordering cost which is submodular. Moreover, items can be held in inventory while incurring a holding cost. The objective is find a sequence of orders that satisfies all demands and minimizes the total ordering and holding costs. (b) Inventory Routing Problem: This involves a single depot that stocks items, and multiple retailer locations facing demands. In each time step, any subset of locations can be visited using a vehicle originating from the depot. There is also cost incurred for holding items at any retailer. The objective here is to satisfy all demands while minimizing the sum of routing and holding costs. We present a unified approach that yields $\mathcal{O}\left(\frac{\log T}{\log\log T}\right)$-factor approximation algorithms for both problems when the holding costs are polynomial functions. A special case is the classic linear holding cost model, wherein this is the first sub-logarithmic approximation ratio for either problem.

cs.DS↗

arXiv2013

Large sets of Kirkman triple systems with order $q^n+2$

The existence of Large sets of Kirkman Triple Systems (LKTS) is an old problem in combinatorics. Known results are very limited, and a lot of them are based on the works of Denniston \cite{MR0349416, MR0369086, MR535159, MR539718}. The only known recursive constructions are an tripling construction by Denniston \cite{MR535159}and a product construction by Lei \cite{MR1931492}, both constructs an LKTS($uv$) on the basis of an LKTS($v$). In this paper, we describe an construction of LKTS$(q^n+2)$ from LKTS$(q+2)$, where $q$ is a prime power of the form $6t+1$. We could construct previous unknown LKTS($v$) by this result, the smallest among them have $v=171,345,363$.

math.CO↗