A (deterministic) polynomial-time algorithm is proposed for approximating the ground state of (general) one-dimensional gapped Hamiltonians. Let , n, η be the energy gap, the system size, and the desired precision, respectively. Neglecting -dependent subpolynomial (in n) and constant factors, the running time of the algorithm is n ) for η = n−O(1) and is n for η = n−o(1).

We develop a fast and accurate variable window approach. The two main ideas for achieving accuracy are choosing a useful range of window sizes/shapes for evaluation and developing a new window cost which is particularly suitable for comparing windows of different sizes. The speed of our approach is due to the Integral Image technique, which allows computation of our window cost over any rectang...

Sklyanin’s method of separation of variables is employed in a calculation of finite temperature expectation values. An essential element of the approach is Baxter’s Q-function. We propose its explicit form corresponding to the ground state of the sinh-Gordon theory. With the method of separation of variables we calculate the finite temperature expectation values of the exponential fields to one...

Space communication systems are plagued by complexity resulting in limited access to orbiting satellites and high mission operation costs that ultimately reduce mission yields and capabilities. In particular, ground stations, the access point between space and terrestrial networks, suffer from monolithic designs, narrow interfaces, and reliability issues that raise significant engineering barri...

These questions contrast the roles of information and complexity in learning. While the two roles share some ground, they are conceptually and technically different. In the common language of learning, the information question is that of generalization and the complexity question is that of scaling. The work of Vapnik and Chervonenkis (1971) provides the key tools for dealing with the informati...

In light of the recently published book Complexity 5 Questions, edited by Carlos Gershenson, I discuss some of the Complexity theories (includingmy own field “Synergetics”)with respect to their applicability to cities. This book,with contributions by 24 leading scientists, shows that there is no general consensus on “Complexity”. Nevertheless, I believe that there is some common ground for an a...

In light of the recently published book Complexity 5 Questions, edited by Carlos Gershenson, I discuss some of the Complexity theories (includingmy own field “Synergetics”)with respect to their applicability to cities. This book,with contributions by 24 leading scientists, shows that there is no general consensus on “Complexity”. Nevertheless, I believe that there is some common ground for an a...

Segmentation of clinically relevant regions from potentially noisy images represents a significant challenge in the field of mammography. We propose novel approaches based on the WaveCluster clustering algorithm for segmenting both the breast profile in the presence of significant acquisition noise and segmenting regions of interest (ROIs) within the breast. Using prior manual segmentations per...

In this paper we discuss ground logics, a family of nonmonotonic modal logics, with the goal of using them in knowledge representation. Ground logics are based on the idea of minimizing the knowledge expressed by non-modal formulae. The nonmonotonic character of the logics can be described either by a x-point equation or by means of a preference relation on possible-worlds models. We address bo...