Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Institucionalització i salut mental

La complexitat de l’atenció de la salut mental i les toxicomanies, en joves institucionalitzats en centres de justícia juvenil, condicionada tant pels propis dèficits de salut, com per les condicions ambientals de l’internament. L’objectiu de la recerca és analitzar la clínica desadaptativa dels joves interns i la seva associació a la presència d’antecedents de consum de tòxics. El disseny de la recerca és un estudi longitudinal de les urgències mèdiques generades en el Centre Educatiu L’Alzina (Barcelona), des de l’1 de gener de 2001 fins el 31 de desembre del mateix any. La metodologia utilitza l’ajust de models multivariants mitjançant Generalized Estimating Equations (GEE) amb error binomial negativa, es calcula el risc de produir-se una demanda per agitació o autolesió, i la seva associació amb la presència d’antecedents de consum de tòxics. Respecte als resultats més destacats: el 59,4% del total de demandes urgents varen ser per episodis d’agitació o autolesió, concentrant-se aquests en el 33% dels interns. Les prevalences de consum de tòxics variaven des d’un 13,2% respecte dels al•lucinògens fins un 71,7% del cannabis, amb un 36,8% de politoxicòmans i un 5,7% d’usuaris de drogues per via parenteral. La població nacional presentà una major prevalença d’hàbits tòxics. Com a principals conclusions de l’estudi, es confirma la hipòtesi general d’una major associació entre antecedents de consum de tòxics i presentació d’episodis de malestar psíquic agut, per bé que limitada al mòdul d’ingrés (inicial). En la resta de grups influirien altres factors, com podria ser la pressió ambiental. Pressió que, almenys en el mòdul intensiu, tot sembla indicar que seria determinant. Els resultats suggereixen doncs, la conveniència de revisar tant les estratègies d’intervenció i abordatge de les toxicomanies, com el disseny ambiental de la institució. S’apunta la necessitat d’investigacions futures amb la incorporació de tècniques qualitatives d’anàlisi. ...

Comparison of quality of life after stereotactic body radiotherapy and surgery for early-stage prostate cancer

Background: As the long-term efficacy of stereotactic body radiation therapy (SBRT) becomes established and other prostate cancer treatment approaches are refined and improved, examination of quality of life (QOL) following prostate cancer treatment is critical in driving both patient and clinical treatment decisions. We present the first study to compare QOL after SBRT and radical prostatectomy, with QOL assessed at approximately the same times pre- and post-treatment and using the same validated QOL instrument. Methods: Patients with clinically localized prostate cancer were treated with either radical prostatectomy (n = 123 Spanish patients) or SBRT (n = 216 American patients). QOL was assessed using the Expanded Prostate Cancer Index Composite (EPIC) grouped into urinary, sexual, and bowel domains. For comparison purposes, SBRT EPIC data at baseline, 3 weeks, 5, 11, 24, and 36 months were compared to surgery data at baseline, 1, 6, 12, 24,and 36 months. Differences in patient characteristics between the two groups were assessed using Chi-squared tests for categorical variables and t-tests for continuous variables. Generalized estimating equation (GEE) models were constructed for each EPIC scale to account for correlation among repeated measures and used to assess the effect of treatment on QOL. Results: The largest differences in QOL occurred in the first 16 months after treatment, with larger declines following surgery in urinary and sexual QOL as compared to SBRT, and a larger decline in bowel QOL following SBRT as compared to surgery. Long-term urinary and sexual QOL declines remained clinically significantly lower for surgery patients but not for SBRT patients. Conclusions: Overall, these results may have implications for patient and physician clinical decision making which are often influenced by QOL. These differences in sexual, urinary and bowel QOL should be closely considered in selecting the right treatment, especially in evaluating the value of non-invasive treatments, such as SBRT.

Comparison of quality of life after stereotactic body radiotherapy and surgery for early-stage prostate cancer

Background: As the long-term efficacy of stereotactic body radiation therapy (SBRT) becomes established and other prostate cancer treatment approaches are refined and improved, examination of quality of life (QOL) following prostate cancer treatment is critical in driving both patient and clinical treatment decisions. We present the first study to compare QOL after SBRT and radical prostatectomy, with QOL assessed at approximately the same times pre- and post-treatment and using the same validated QOL instrument. Methods: Patients with clinically localized prostate cancer were treated with either radical prostatectomy (n = 123 Spanish patients) or SBRT (n = 216 American patients). QOL was assessed using the Expanded Prostate Cancer Index Composite (EPIC) grouped into urinary, sexual, and bowel domains. For comparison purposes, SBRT EPIC data at baseline, 3 weeks, 5, 11, 24, and 36 months were compared to surgery data at baseline, 1, 6, 12, 24,and 36 months. Differences in patient characteristics between the two groups were assessed using Chi-squared tests for categorical variables and t-tests for continuous variables. Generalized estimating equation (GEE) models were constructed for each EPIC scale to account for correlation among repeated measures and used to assess the effect of treatment on QOL. Results: The largest differences in QOL occurred in the first 1-6 months after treatment, with larger declines following surgery in urinary and sexual QOL as compared to SBRT, and a larger decline in bowel QOL following SBRT as compared to surgery. Long-term urinary and sexual QOL declines remained clinically significantly lower for surgery patients but not for SBRT patients. Conclusions: Overall, these results may have implications for patient and physician clinical decision making which are often influenced by QOL. These differences in sexual, urinary and bowel QOL should be closely considered in selecting the right treatment, especially in evaluating the value of non-invasive treatments, such as SBRT.

Predictors of remission in the treatment of major depressive disorder: real-world evidence from a 6-month prospective observational study

BACKGROUND: This study examined potential predictors of remission among patients treated for major depressive disorder (MDD) in a naturalistic clinical setting, mostly in the Middle East, East Asia, and Mexico. METHODS: Data for this post hoc analysis were taken from a 6-month prospective, noninterventional, observational study that involved 1,549 MDD patients without sexual dysfunction at baseline in 12 countries worldwide. Depression severity was measured using the Clinical Global Impression of Severity and the 16-item Quick Inventory of Depressive Symptomatology Self-Report (QIDS-SR16). Depression-related pain was measured using the pain-related items of the Somatic Symptom Inventory. Remission was defined as a QIDS-SR16 score ≤5. Generalized estimating equation regression models were used to examine baseline factors associated with remission during follow-up. RESULTS: Being from East Asia (odds ratio [OR] 0.48 versus Mexico; P<0.001), a higher level of depression severity at baseline (OR 0.77, P=0.003, for Clinical Global Impression of Severity; OR 0.92, P<0.001, for QIDS-SR16), more previous MDD episodes (OR 0.92, P=0.007), previous treatments/therapies for depression (OR 0.78, P=0.030), and having any significant psychiatric and medical comorbidity at baseline (OR 0.60, P<0.001) were negatively associated with remission, whereas being male (OR 1.29, P=0.026) and treatment with duloxetine (OR 2.38 versus selective serotonin reuptake inhibitors, P<0.001) were positively associated with remission. However, the association between Somatic Symptom Inventory pain scores and remission no longer appeared to be significant in this multiple regression (P=0.580), (P=0.008 in descriptive statistics), although it remained significant in a subgroup of patients treated with selective serotonin reuptake inhibitors (OR 0.97, P=0.023), but not in those treated with duloxetine (P=0.182). CONCLUSION: These findings are largely consistent with previous reports from the USA and Europe. They also highlight the potential mediating role of treatment with duloxetine on the negative relationship between depression-related pain and outcomes of depression.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Optimal generalized quantum measurements for arbitrary spin systems

Positive-operator-valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal positive-operator-valued measurement for the N=2 case, a rigorous bound for N=3, and set up the analysis for arbitrary N.

Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

Generalized percolation in random directed networks

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edgesthat is, edges pointing in both directions simultaneously. These two ingredients alter the previously known scenario and open new views and perspectives on percolation phenomena. Equations for the percolation threshold and the sizes of the giant components are derived in the most general case. We also present simulation results for a particular example of uncorrelated network with bidirectional edges confirming the theoretical predictions.

Petrou type-D perfect-fluid solutions in generalized Kerr-Schild form.

Generalized KerrSchild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.