Ueber die Darstellung der Dreieckesfunktion durch die Poincarésche [theta]-Reihe /

Curriculum vitae.

Transformation der hyperelliptischen Functionen P = 2 und ihre Bedeutung für die Kummersche Fläche /

Includes his Betrachtungen über die Kummer'sche Fläche und ihren Zusammenhang mit den hyperelliptischen Functionen p = 2. München : Akademische Buchdruckerei von F. Straub, 1878. 59 p.

Thetafunktionen und hyperelliptische funktionen,

Available on demand as hard copy or computer file from Cornell University Library.

Theorie der zweifach unendlichen Thetareihen auf Grund der Riemann'schen Thetaformel.

Available on demand as hard copy or computer file from Cornell University Library.

Untersuchungen ueber die Riemann'sche thetaformel und die Riemann'sche charakteristikentheorie.

Available on demand as hard copy or computer file from Cornell University Library.

Neue grundlagen einer Theorie der allgemeinen Thetafunctionen,

Available on demand as hard copy or computer file from Cornell University Library.

Kummer's quartic surface,

Prefatory note by H.F. Baker.

Time and Energy Complexity of Distributed Computation of a Class of Functions in Wireless Sensor Networks

We consider a scenario in which a wireless sensor network is formed by randomly deploying n sensors to measure some spatial function over a field, with the objective of computing a function of the measurements and communicating it to an operator station. We restrict ourselves to the class of type-threshold functions (as defined in the work of Giridhar and Kumar, 2005), of which max, min, and indicator functions are important examples: our discussions are couched in terms of the max function. We view the problem as one of message-passing distributed computation over a geometric random graph. The network is assumed to be synchronous, and the sensors synchronously measure values and then collaborate to compute and deliver the function computed with these values to the operator station. Computation algorithms differ in (1) the communication topology assumed and (2) the messages that the nodes need to exchange in order to carry out the computation. The focus of our paper is to establish (in probability) scaling laws for the time and energy complexity of the distributed function computation over random wireless networks, under the assumption of centralized contention-free scheduling of packet transmissions. First, without any constraint on the computation algorithm, we establish scaling laws for the computation time and energy expenditure for one-time maximum computation. We show that for an optimal algorithm, the computation time and energy expenditure scale, respectively, as Theta(radicn/log n) and Theta(n) asymptotically as the number of sensors n rarr infin. Second, we analyze the performance of three specific computation algorithms that may be used in specific practical situations, namely, the tree algorithm, multihop transmission, and the Ripple algorithm (a type of gossip algorithm), and obtain scaling laws for the computation time and energy expenditure as n rarr infin. In particular, we show that the computation time for these algorithms scales as Theta(radicn/lo- g n), Theta(n), and Theta(radicn log n), respectively, whereas the energy expended scales as , Theta(n), Theta(radicn/log n), and Theta(radicn log n), respectively. Finally, simulation results are provided to show that our analysis indeed captures the correct scaling. The simulations also yield estimates of the constant multipliers in the scaling laws. Our analyses throughout assume a centralized optimal scheduler, and hence, our results can be viewed as providing bounds for the performance with practical distributed schedulers.

Cross-correlation of excitation functions for different fragments and different scattering angles in Al-27(F-19, x)y reactions

Excitation functions have been measured for different projectile-like fragments produced in Al-27(F-19,x)y reactions at incident energies from 110.25 to 118.75 MeV in 250 keV steps. Strong cross section fluctuations of the excitation functions are observed. The cross- correlation coefficients of the excitation functions for different atomic number Z and for different scattering angle theta(cm) have been deduced. These coefficients are much larger than the statistical theoretical calculated ones. This indicates that there are strong correlations between different exit channels in the dissipative heavy ion Collision of Al-27(F-19,x)y.

Selective Coupling between Theta Phase and Neocortical Fast Gamma Oscillations during REM-Sleep in Mice

TORT, A. B. L. ; SCHEFFER-TEIXEIRA, R ; Souza, B.C. ; DRAGUHN, A. ; BRANKACK, J. . Theta-associated high-frequency oscillations (110-160 Hz) in the hippocampus and neocortex. Progress in Neurobiology , v. 100, p. 1-14, 2013.

SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS

Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.

Neural basis of visual deficits recovery: visual residual functions and multisensory integration.

The ability of integrating into a unified percept sensory inputs deriving from different sensory modalities, but related to the same external event, is called multisensory integration and might represent an efficient mechanism of sensory compensation when a sensory modality is damaged by a cortical lesion. This hypothesis has been discussed in the present dissertation. Experiment 1 explored the role of superior colliculus (SC) in multisensory integration, testing patients with collicular lesions, patients with subcortical lesions not involving the SC and healthy control subjects in a multisensory task. The results revealed that patients with collicular lesions, paralleling the evidence of animal studies, demonstrated a loss of multisensory enhancement, in contrast with control subjects, providing the first lesional evidence in humans of the essential role of SC in mediating audio-visual integration. Experiment 2 investigated the role of cortex in mediating multisensory integrative effects, inducing virtual lesions by inhibitory theta-burst stimulation on temporo-parietal cortex, occipital cortex and posterior parietal cortex, demonstrating that only temporo-parietal cortex was causally involved in modulating the integration of audio-visual stimuli at the same spatial location. Given the involvement of the retino-colliculo-extrastriate pathway in mediating audio-visual integration, the functional sparing of this circuit in hemianopic patients is extremely relevant in the perspective of a multisensory-based approach to the recovery of unisensory defects. Experiment 3 demonstrated the spared functional activity of this circuit in a group of hemianopic patients, revealing the presence of implicit recognition of the fearful content of unseen visual stimuli (i.e. affective blindsight), an ability mediated by the retino-colliculo-extrastriate pathway and its connections with amygdala. Finally, Experiment 4 provided evidence that a systematic audio-visual stimulation is effective in inducing long-lasting clinical improvements in patients with visual field defect and revealed that the activity of the spared retino-colliculo-extrastriate pathway is responsible of the observed clinical amelioration, as suggested by the greater improvement observed in patients with cortical lesions limited to the occipital cortex, compared to patients with lesions extending to other cortical areas, found in tasks high demanding in terms of spatial orienting. Overall, the present results indicated that multisensory integration is mediated by the retino-colliculo-extrastriate pathway and that a systematic audio-visual stimulation, activating this spared neural circuit, is able to affect orientation towards the blind field in hemianopic patients and, therefore, might constitute an effective and innovative approach for the rehabilitation of unisensory visual impairments.

Decreased functional connectivity of EEG theta-frequency activity in first-episode, neuroleptic-naïve patients with schizophrenia: preliminary results

We explored and refined the hypothesis that during a first episode of acute schizophrenia a disorganization of brain functioning is present. A novel EEG measure was introduced, Global Field Synchronization (GFS), that estimates functional connectivity of brain processes in different EEG frequency bands. The measure was applied to EEG's from 11 never-treated, first-episode, young patients with an acute, positive, schizophrenic symptomatology and from 19 controls, residing in Bern, Switzerland. In comparison to age- and sex- matched controls, patients had significantly decreased GFS in the theta EEG frequency band, indicating a loosened functional connectivity of processes in this frequency. The result was confirmed in an independent, comparable patient group from Osaka, Japan (9 patients and 9 controls), thus making a total of 20 analyzed patients. Previous EEG research in healthy, awake subjects indicated a positive correlation of theta activity with memory functions. Thus, our result suggests a loss of mutual interdependence of memory functions in patients with acute schizophrenia, which agrees well with previous reports of working memory dysfunction in schizophrenia.

Improved slope adjustment functions for soil erosion prediction

Numerous studies in the last 60 years have investigated the relationship between land slope and soil erosion rates. However, relatively few of these have investigated slope gradient responses: ( a) for steep slopes, (b) for specific erosion processes, and ( c) as a function of soil properties. Simulated rainfall was applied in the laboratory on 16 soils and 16 overburdens at 100 mm/h to 3 replicates of unconsolidated flume plots 3 m long by 0.8 m wide and 0.15 m deep at slopes of 20, 5, 10, 15, and 30% slope in that order. Sediment delivery at each slope was measured to determine the relationship between slope steepness and erosion rate. Data from this study were evaluated alongside data and existing slope adjustment functions from more than 55 other studies from the literature. Data and the literature strongly support a logistic slope adjustment function of the form S = A + B/[1 + exp (C - D sin theta)] where S is the slope adjustment factor and A, B, C, and D are coefficients that depend on the dominant detachment and transport processes. Average coefficient values when interill-only processes are active are A - 1.50, B 6.51, C 0.94, and D 5.30 (r(2) = 0.99). When rill erosion is also potentially active, the average slope response is greater and coefficient values are A - 1.12, B 16.05, C 2.61, and D 8.32 (r(2) = 0.93). The interill-only function predicts increases in sediment delivery rates from 5 to 30% slope that are approximately double the predictions based on existing published interill functions. The rill + interill function is similar to a previously reported value. The above relationships represent a mean slope response for all soils, yet the response of individual soils varied substantially from a 2.5-fold to a 50-fold increase over the range of slopes studied. The magnitude of the slope response was found to be inversely related ( log - log linear) to the dispersed silt and clay content of the soil, and 3 slope adjustment equations are proposed that provide a better estimate of slope response when this soil property is known. Evaluation of the slope adjustment equations proposed in this paper using independent datasets showed that the new equations can improve soil erosion predictions.

Selective Coupling between Theta Phase and Neocortical Fast Gamma Oscillations during REM-Sleep in Mice

TORT, A. B. L. ; SCHEFFER-TEIXEIRA, R ; Souza, B.C. ; DRAGUHN, A. ; BRANKACK, J. . Theta-associated high-frequency oscillations (110-160 Hz) in the hippocampus and neocortex. Progress in Neurobiology , v. 100, p. 1-14, 2013.