Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.Comment: A semi-exactly solvable model (half of the eigenstates are in the Bethe form

Directly Indecomposables in Semidegenerate Varieties of Connected po-Groupoids

We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the SRP have definable factor congruences and if the similarity type is finite, directly indecomposables are axiomatizable by a set of first-order sentences. We obtain such a set for semidegenerate varieties of connected po-groupoids and show its quantifier complexity is bounded in general

The moduli space of hypersurfaces whose singular locus has high dimension

Let $k$ be an algebraically closed field and let $b$ and $n$ be integers with $n\geq 3$ and $1\leq b \leq n-1.$ Consider the moduli space $X$ of hypersurfaces in $\mathbb{P}^n_k$ of fixed degree $l$ whose singular locus is at least $b$-dimensional. We prove that for large $l$, $X$ has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear $b$-dimensional subspace of $\mathbb{P}^n$. The proof will involve a probabilistic counting argument over finite fields.Comment: Final version, including the incorporation of all comments by the refere

Tone-activated, remote, alert communication system

Pocket sized transmitter, frequency modulated by crystal derived tones, with integral loop antenna provides police with easy operating alert signal communicator which uses patrol car radio to relay signal. Communication channels are time shared by several patrol units

Ferromagnetism in the two dimensional t-t' Hubbard model at the Van Hove density

Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping t and next-nearest-neighbor hopping t', by simulation of lattices with up to 20 X 20 sites. For a given R=2t'/t, we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for R=0.94 (R=0.2). This is consistent with the prediction of the T-matrix approximation, which sums the most singular set of diagrams.Comment: 10 pages, RevTeX 3.0 + a single postscript file with all figure

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio

Controlled Radiation Capsule for Precision and Rapid Cancer Treatment

This research aims to transform cancer treatment through the optimization of brachytherapy, with a focus on reducing treatment duration, setup complexities, and financial burdens, all while emphasizing patient safety. Patients living at a distance from radiation clinics, particularly those undergoing extended Low Dose Radiation brachytherapy, often struggle with the formidable financial challenges associated with securing nearby accommodations. In response to these issues, the research introduces a radiation capsule designed to condense the conventional six-month treatment period to approximately just one week, thereby significantly reducing the duration of required accommodations. This capsule is especially relevant considering the construction cost of $40 million for a single-room proton therapy system, a financial hurdle that affects countless patients. The radiation capsule employs minimally invasive procedures, eliminating the need for invasive probing, marking a departure from conventional High Dose Radiation brachytherapy treatments. It harnesses wireless power transfer technology, ensuring seamless energy transfer from an external planar rectangular coil to an internal coil, both reinforced with Metglas sheets to amplify magnetic field strength. A built-in safety mechanism ensures the capsule automatically closes in the absence of current, thereby guaranteeing patient well-being. However, the most interesting aspect of this research is the introduction of Medium Dose Radiation (MDR), which bridges the treatment gap between High Dose Radiation (HDR) and Low Dose Radiation (LDR), significantly reducing radiation hazards while shortening treatment durations to a matter of days. This research introduces improvements in cancer treatment, enhancing accessibility, efficiency, and patient safety. By introducing MDR therapy, it not only eases the financial burdens of patients but also ensures shorter treatment times, making cancer treatment more efficient and patient centered

Understanding natural language commands for robotic navigation and mobile manipulation

This paper describes a new model for understanding natural language commands given to autonomous systems that perform navigation and mobile manipulation in semi-structured environments. Previous approaches have used models with fixed structure to infer the likelihood of a sequence of actions given the environment and the command. In contrast, our framework, called Generalized Grounding Graphs, dynamically instantiates a probabilistic graphical model for a particular natural language command according to the command's hierarchical and compositional semantic structure. Our system performs inference in the model to successfully find and execute plans corresponding to natural language commands such as "Put the tire pallet on the truck." The model is trained using a corpus of commands collected using crowdsourcing. We pair each command with robot actions and use the corpus to learn the parameters of the model. We evaluate the robot's performance by inferring plans from natural language commands, executing each plan in a realistic robot simulator, and asking users to evaluate the system's performance. We demonstrate that our system can successfully follow many natural language commands from the corpus

Approaching the Symbol Grounding Problem with Probabilistic Graphical Models

In order for robots to engage in dialog with human teammates, they must have the ability to map between words in the language and aspects of the external world. A solution to this symbol grounding problem (Harnad, 1990) would enable a robot to interpret commands such as “Drive over to receiving and pick up the tire pallet.” In this article we describe several of our results that use probabilistic inference to address the symbol grounding problem. Our specific approach is to develop models that factor according to the linguistic structure of a command. We first describe an early result, a generative model that factors according to the sequential structure of language, and then discuss our new framework, generalized grounding graphs (G3). The G3 framework dynamically instantiates a probabilistic graphical model for a natural language input, enabling a mapping between words in language and concrete objects, places, paths and events in the external world. We report on corpus-based experiments where the robot is able to learn and use word meanings in three real-world tasks: indoor navigation, spatial language video retrieval, and mobile manipulation.U.S. Army Research Laboratory. Collaborative Technology Alliance Program (Cooperative Agreement W911NF-10-2-0016)United States. Office of Naval Research (MURI N00014-07-1-0749