Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil

Editorial: Videos in der (Hochschul-)Lehre

24.04.2014 | Thomas Antretter, Johannes Dorfinger, Martin Ebner, Michael Kopp, Walther Nagler, Jutta Pauschenwein, Michael Raunig, Manfred Rechberger, Herwig Rehatschek, Patrick Schweighofer, Reinhard Staber & Martin Teufel (Graz

Solvation free energy profile of the SCN- ion across the water-1,2-dichloroethane liquid/liquid interface. A computer simulation study

The solvation free energy profile of a single SCN- ion is calculated across the water-1,2-dichloroethane liquid/liquid interface at 298 K by the constraint force method. The obtained results show that the free energy cost of transferring the ion from the aqueous to the organic phase is about 70 kJ/mol, The free energy profile shows a small but clear well at the aqueous side of the interface, in the subsurface region of the water phase, indicating the ability of the SCN- ion to be adsorbed in the close vicinity of the interface. Upon entrance of the SCN- ion to the organic phase a coextraction of the water molecules of its first hydration shell occurs. Accordingly, when it is located at the boundary of the two phases the SCN- ion prefers orientations in which its bulky S atom is located at the aqueous side, and the small N atom, together with its first hydration shell, at the organic side of the interface

Using Linguistic Information and Machine Learning Techniques to Identify Entities from Juridical Documents

Information extraction from legal documents is an important and open problem. A mixed approach, using linguistic information and machine learning techniques, is described in this paper. In this approach, top-level legal concepts are identified and used for document classifica- tion using Support Vector Machines. Named entities, such as, locations, organizations, dates, and document references, are identified using se- mantic information from the output of a natural language parser. This information, legal concepts and named entities, may be used to popu- late a simple ontology, allowing the enrichment of documents and the creation of high-level legal information retrieval systems. The proposed methodology was applied to a corpus of legal documents - from the EUR-Lex site – and it was evaluated. The obtained results were quite good and indicate this may be a promising approach to the legal information extraction problem

Stroke Rehabilitation Reaches a Threshold

Motor training with the upper limb affected by stroke partially reverses the loss of cortical representation after lesion and has been proposed to increase spontaneous arm use. Moreover, repeated attempts to use the affected hand in daily activities create a form of practice that can potentially lead to further improvement in motor performance. We thus hypothesized that if motor retraining after stroke increases spontaneous arm use sufficiently, then the patient will enter a virtuous circle in which spontaneous arm use and motor performance reinforce each other. In contrast, if the dose of therapy is not sufficient to bring spontaneous use above threshold, then performance will not increase and the patient will further develop compensatory strategies with the less affected hand. To refine this hypothesis, we developed a computational model of bilateral hand use in arm reaching to study the interactions between adaptive decision making and motor relearning after motor cortex lesion. The model contains a left and a right motor cortex, each controlling the opposite arm, and a single action choice module. The action choice module learns, via reinforcement learning, the value of using each arm for reaching in specific directions. Each motor cortex uses a neural population code to specify the initial direction along which the contralateral hand moves towards a target. The motor cortex learns to minimize directional errors and to maximize neuronal activity for each movement. The derived learning rule accounts for the reversal of the loss of cortical representation after rehabilitation and the increase of this loss after stroke with insufficient rehabilitation. Further, our model exhibits nonlinear and bistable behavior: if natural recovery, motor training, or both, brings performance above a certain threshold, then training can be stopped, as the repeated spontaneous arm use provides a form of motor learning that further bootstraps performance and spontaneous use. Below this threshold, motor training is “in vain”: there is little spontaneous arm use after training, the model exhibits learned nonuse, and compensatory movements with the less affected hand are reinforced. By exploring the nonlinear dynamics of stroke recovery using a biologically plausible neural model that accounts for reversal of the loss of motor cortex representation following rehabilitation or the lack thereof, respectively, we can explain previously hard to reconcile data on spontaneous arm use in stroke recovery. Further, our threshold prediction could be tested with an adaptive train–wait–train paradigm: if spontaneous arm use has increased in the “wait” period, then the threshold has been reached, and rehabilitation can be stopped. If spontaneous arm use is still low or has decreased, then another bout of rehabilitation is to be provided

Rapid generation of human B-cell lymphomas via combined expression of Myc and Bcl2 and their use as a preclinical model for biological therapies

Although numerous mouse models of B-cell malignancy have been developed via the enforced expression of defined oncogenic lesions, the feasibility of generating lineage-defined human B-cell malignancies using mice reconstituted with modified human hematopoietic stem cells (HSCs) remains unclear. In fact, whether human cells can be transformed as readily as murine cells by simple oncogene combinations is a subject of considerable debate. Here, we describe the development of humanized mouse model of MYC/BCL2-driven ‘double-hit’ lymphoma. By engrafting human HSCs transduced with the oncogene combination into immunodeficient mice, we generate a fatal B malignancy with complete penetrance. This humanized-MYC/BCL2-model (hMB) accurately recapitulates the histopathological and clinical aspects of steroid-, chemotherapy- and rituximab-resistant human ‘double-hit’ lymphomas that involve the MYC and BCL2 loci. Notably, this model can serve as a platform for the evaluation of antibody-based therapeutics. As a proof of principle, we used this model to show that the anti-CD52 antibody alemtuzumab effectively eliminates lymphoma cells from the spleen, liver and peripheral blood, but not from the brain. The hMB humanized mouse model underscores the synergy of MYC and BCL2 in ‘double-hit’ lymphomas in human patients. Additionally, our findings highlight the utility of humanized mouse models in interrogating therapeutic approaches, particularly human-specific monoclonal antibodies.Kathy and Curt Marble Cancer Research FundSingapore-MIT Alliance for Research and TechnologyNational Institutes of Health (U.S.) (Grant R01-CA128803)Virginia and Daniel K. Ludwig Graduate FellowshipNational Institute of General Medical Sciences (U.S.) (Medical Scientist Training Program Grant T32GM007753)MIT School of Science (Cancer Research Fellowship

A semidefinite programming approach for solving multiobjective linear programming

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudopolynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.Junta de AndalucíaFondo Europeo de Desarrollo RegionalMinisterio de Ciencia e Innovació

Intrinsic structure and dynamics of the water/nitrobenzene interface

In this paper we present results of a detailed and systematic molecular dynamics study of the water/nitrobenzene interface. Using a simple procedure to eliminate fluctuations of the interface position, we are able to obtain true intrinsic profiles for several properties (density, hydrogen bonds, molecular orientation, etc.) in the direction perpendicular to the interfacial plane. Our results show that both water and organic inter-facial molecules form a tightly packed layer oriented parallel to the interface, with reduced mobility in the perpendicular direction. Beyond this layer, water quickly restores its bulk structure, while nitrobenzene exhibits structural anisotropies that extend further into the bulk region: Water molecules that protrude farthest into the organic phase point one hydrogen atom in the direction perpendicular to the interface, forming a hydrogen bond with a nitrobenzene oxygen. By fitting both the global and the intrinsic density profiles, we obtain estimates for the total and intrinsic interface widths, respectively. These are combined with capillary wave theory to produce a self-consistent method for the calculation of the inter-facial tension. Values calculated using this method are in very good agreement with direct calculations from the components of the pressure tensor

Graz Endocrine Causes of Hypertension (GECOH) study: a diagnostic accuracy study of aldosterone to active renin ratio in screening for primary aldosteronism

<p>Abstract</p> <p>Background</p> <p>Primary aldosteronism (PA) affects approximately 5 to 10% of all patients with arterial hypertension and is associated with an excess rate of cardiovascular complications that can be significantly reduced by a targeted treatment. There exists a general consensus that the aldosterone to renin ratio should be used as a screening tool but valid data about the accuracy of the aldosterone to renin ratio in screening for PA are sparse. In the Graz endocrine causes of hypertension (GECOH) study we aim to prospectively evaluate diagnostic procedures for PA.</p> <p>Methods and design</p> <p>In this single center, diagnostic accuracy study we will enrol 400 patients that are routinely referred to our tertiary care center for screening for endocrine hypertension. We will determine the aldosterone to active renin ratio (AARR) as a screening test. In addition, all study participants will have a second determination of the AARR and will undergo a saline infusion test (SIT) as a confirmatory test. PA will be diagnosed in patients with at least one AARR of ≥ 5.7 ng/dL/ng/L (including an aldosterone concentration of ≥ 9 ng/dL) who have an aldosterone level of ≥ 10 ng/dL after the saline infusion test. As a primary outcome we will calculate the receiver operating characteristic curve of the AARR in diagnosing PA. Secondary outcomes include the test characteristics of the saline infusion test involving a comparison with 24 hours urine aldosterone levels and the accuracy of the aldosterone to renin activity ratio in diagnosing PA. In addition we will evaluate whether the use of beta-blockers significantly alters the accuracy of the AARR and we will validate our laboratory methods for aldosterone and renin.</p> <p>Conclusion</p> <p>Screening for PA with subsequent targeted treatment is of great potential benefit for hypertensive patients. In the GECOH study we will evaluate a standardised procedure for screening and diagnosing of this disease.</p