Extention of Apolarity and Grace Theorem

MSC 2010: 30C10

Algebraic duality theorems for infinite LP problems

In this paper we consider a primal-dual infinite linear programming problem-pair, i.e. LPs on infinite dimensional spaces with infinitely many constraints. We present two duality theorems for the problem-pair: a weak and a strong duality theorem. We do not assume any topology on the vector spaces, therefore our results are algebraic duality theorems. As an application, we consider transferable utility cooperative games with arbitrarily many players.

Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

Hearing Preservation And Cochlear Implants According To Inner Ear Approach: Multicentric Evaluation.

Electroacoustic stimulation is an excellent option for people with residual hearing in the low frequencies, who obtain insufficient benefit with hearing aids. To be effective, the subject's residual hearing should be preserved during cochlear implant surgery. To evaluate the hearing preservation in patients that underwent implant placement and to compare the results in accordance with the approach to the inner ear. 19 subjects underwent a soft surgical technique, and the electrode MED-EL FLEX™ EAS, designed to be atraumatic, was used. We evaluated pre- and postoperative tonal audiometric tests with an average of 18.4 months after implantation, to measure the rate of hearing preservation. 17 patients had total or partial preservation of residual hearing; 5 had total hearing preservation and two individuals had no preservation of hearing. The insertion of the electrode occurred through a cochleostomy in 3 patients, and in 2 of these there was no hearing preservation; the other 16 patients experienced electrode insertion through a round window approach. All patients benefited from the cochlear implant, even those who are only using electrical stimulation. The hearing preservation occurred in 89.4% of cases. There was no significant difference between the forms of inner ear approach.

[preservation Of The Fertility And The Ovaries In Women With Benign Adnexal Tumors].

To evaluate the sparing of fertility and ovaries in women submitted to surgical treatment for benign adnexal tumors. Between February 2010 and January 2014, 206 patients were included in this observational study as they were submitted to surgical treatment for benign ovarian tumors at CAISM, a tertiary hospital. Fertility sparing surgery was defined as tumorectomy or unilateral salpingoophorectomy without hysterectomy in premenopausal women. Preservation of the ovary occurred when at least one ovary or part of it was mantained. Of the 206 women with benign tumors, 120 (58%) were premenopausal and 86 (42%) were postmenopausal. There were 36 (30%) ovarian germ cell tumors, 31 (26%) epithelial neoplasms and 11 (9%) sex-cord stromal tumors among premenopausal women. In the group of postmenopausal women, 35 (41%) epithelial neoplasms, 27 (31%) sex-cord stromal tumors and 8 (9%) ovarian germ cell tumors were identified. Among 36 women with non-neoplastic ovarian tumors, 21 (58%) had endometriomas and 8 (22%) functional cysts. Among 22 women with extra-ovarian tumors, uterine leiomyomatosis was the most frequent finding (50%). In the group of women who were ≤ 35 years old, 26 (57%) were treated by tumorectomy and 18 (39%) were submitted to unilateral salpingoophorectomy with sparing of the uterus and the contralateral ovary. Women who were ≤ 35 years old were more frequently operated by laparoscopy which was associated with a higher number of fertility sparing procedures when compared to laparotomy (p<0.01). Twenty-six (28%) women submitted to hysterectomy with bilateral salpingoophorectomy were premenopausal. Although there is a trend to perform only tumorectomy in women who are ≤ 35 years old, a significant number of young women is still treated by salpingoophorectomy. Among 36- to 45-year-old women, only 70% had their fertility spared, while 20% had both ovaries removed. However, whenever possible, we must try to preserve the ovaries, mainly in premenopausal women.

Preservation Of The External Jugular Vein In Bilateral Radical Neck Dissections: Technique In Two Cases And Review Of The Literature.

Context. The possibility of cephalic venous hypertension with the resultant facial edema and elevated cerebrospinal fluid pressure continues to challenge head and neck surgeons who perform bilateral radical neck dissections during simultaneous or staged procedures. Case Report. The staged procedure in patients who require bilateral neck dissections allows collateral venous drainage to develop, mainly through the internal and external vertebral plexuses, thereby minimizing the risks of deleterious consequences. Nevertheless, this procedure has disadvantages, such as a delay in definitive therapy, the need for a second hospitalization and anesthesia, and the risk of cutting lymphatic vessels and spreading viable cancer cells. In this paper, we discuss the rationale and feasibility of preserving the external jugular vein. Considering the limited number of similar reports in the literature, two cases in which this procedure was accomplished are described. The relevant anatomy and technique are reviewed and the patients' outcomes are discussed. Conclusion. Preservation of the EJV during bilateral neck dissections is technically feasible, fast, and safe, with clinically and radiologically demonstrated patency.

Fundamentos geometricos e algebricos da calibração e reconstrução tridimensional : aplicação na analise cinematica de movimentos humanos

Universidade Estadual de Campinas . Faculdade de Educação Física

A Goldstone theorem in thermal relativistic quantum field theory

We prove a Goldstone theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of spacelike decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed. (C) 2011 American Institute of Physics. [doi:10.1063/1.3526961]

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

Long-term preservation of Neozygites tanajoae (Entomophthorales : Neozygitaceae) in cadavers of Mononychellus tanajoae (Acari : Tetranychidae)

To determine the effect of storage on fungal survival, mummified cadavers of the cassava green mite pathogen, Neozygites tanajoae were placed at different conditions of temperature and relative humidity. The best condition for long-term preservation was -10 degrees C. At this condition, the fungus retained viability for 10 years when the experiment was terminated, with a decrease in sporulation with time. Cadavers placed at 4 degrees C and 5% RH sporulated for 2 years, while the fungus survived for only 7 days at 25 degrees C and 50% RH.

Preservation of Phakopsora pachyrhizi uredospores

This study compared different temperatures and dormancy-reversion procedures for preservation of Phakopsora pachyrhizi uredospores. The storage temperatures tested were room temperature, 5 degrees C, -20 degrees C and -80 degrees C. Dehydrated and non-dehydrated uredospores were used, and evaluations for germination (%) and infectivity (no. of lesions/cm(2)) were made with fresh harvested spores and after 15, 29 76, 154 and 231 days of storage. The dormancy-reversion procedures evaluated were thermal shock (40 degrees C/5 min) followed or not by hydration (moist chamber,24 h). Uredospores stored at room temperature were viable only up to a month of storage, regardless of their hydration condition. Survival of uredospores increased with storage at lower temperatures. Dehydration of uredospores prior to storage increased their viability, mainly for uredospores stored at 5 degrees C, -20 degrees C and -80 degrees C. At 5 degrees C and -20 degrees C, dehydrated uredospores showed increases in viability of at least 47 and 127 days, respectively, compared to non-dehydrated spores. Uredospore germination and infectivity after storage for 231 days (7.7 months), could only be observed at -80 degrees C, for both hydration conditions. At this storage temperature, dehydrated and non-dehydrated uredospores exhibited 56 and 28% of germination at the end of the experiment, respectively. Storage at -80 degrees C also maintained uredospore infectivity, based upon levels of Infection frequency, for both hydration conditions. Among the dormancy-reversion treatments applied to spores stored at -80 degrees C, those involving hydration allowed recoveries of 85 to 92% of the initial germination.

Libido Operandi or Conflict: Tafuri on Historic Preservation and Historiography

A brief analysis of an interview with Manfredo Tafuri (1991) on the relationship between historiography and judgements bound up in architectural preservation, restoration and conservation.