Reduction of Linear Systems of ODEs with Optimal Replacement Variables

2011 ◽  
Vol 9 (3) ◽  
pp. 756-779
Author(s):  
Alex Solomonoff ◽  
Wai Sun Don
Keyword(s):  
Linear Systems ◽  
Ad Hoc ◽  
Original System ◽  
Linear Combinations ◽  
Optimal Replacement ◽  
Small Set ◽  
Systems Of Odes ◽  
The Difference ◽  
Linear Odes ◽  
Linear Pdes

AbstractIn this exploratory study, we present a new method of approximating a large system of ODEs by one with fewer equations, while attempting to preserve the essential dynamics of a reduced set of variables of interest. The method has the following key elements: (i) put a (simple, ad-hoc) probability distribution on the phase space of the ODE; (ii) assert that a small set of replacement variables are to be unknown linear combinations of the not-of-interest variables, and let the variables of the reduced system consist of the variables-of-interest together with the replacement variables; (iii) find the linear combinations that minimize the difference between the dynamics of the original system and the reduced system. We describe this approach in detail for linear systems of ODEs. Numerical techniques and issues for carrying out the required minimization are presented. Examples of systems of linear ODEs and variable-coefficient linear PDEs are used to demonstrate the method. We show that the resulting approximate reduced system of ODEs gives good approximations to the original system. Finally, some directions for further work are outlined.

Patterns of care in Italian psychiatric services and psychosocial outcome of schizophrenic patients. A three-year prospective study

1989 ◽  
Vol 4 (1) ◽  
pp. 23-31 ◽  
Author(s):  
D. Kemali ◽  
M. Maj ◽  
B. Carpiniello ◽  
R.D. Giurazza ◽  
M. Impagnatiello ◽  
...  
Keyword(s):  
Psychosocial Adjustment ◽  
Ad Hoc ◽  
Social Withdrawal ◽  
Skills Training ◽  
Favourable Outcome ◽  
Stepwise Logistic Regression ◽  
Psychosocial Outcome ◽  
Stepwise Logistic Regression Analysis ◽  
Schizophrenic Patients ◽  
The Difference

Summary141 patients with an ICD-9 diagnosis of schizophrenic psychosis were followed up prospectively for 3 years in 7 Italian centres, representative of the different degrees of application of the psychiatric reform law (Law 180) passed in 1978. It was agreed that each centre would treat the patients according to its routine, and that all contacts with the patients and each intervention performed would be carefully recorded in an ad hoc schedule. The baseline evaluation of psychosocial adjustment was performed by the Disability Assessment Schedule (DAS), and this assessment was then repeated every 6 months during the follow-up period. At the end of this period, the rating on the DAS section 5 was taken as a global measure of patients’ psychosocial outcome. On a stepwise logistic regression analysis, 2 variables were found to be significantly predictive of psychosocial outcome, that is the use of social and/or vocational skills training (associated with a favourable outcome) and the number of days/year of full hospitalization (associated with a poor outcome). Trieste and Arezzo were the only centres in which a significant improvement of the score on some DAS subscales (namely, “occupational role, interest” and “social withdrawal”) was detected. In the whole patient sample, the difference between the final and the baseline score on these subscales correlated significantly with the number/year of outpatient contacts and of home visits. These findings confirm the favourable impact of the community-oriented care provided in some Italian centres on the Psychosocial outcome of schizophrenic patients.

scholarly journals Allometric Equations for Estimating Biomass and Carbon Stocks in Afforested Open Woodlands with Black Spruce and Jack Pine, in the Eastern Canadian Boreal Forest

Forests ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 59
Author(s):  
Olivier Fradette ◽  
Charles Marty ◽  
Pascal Tremblay ◽  
Daniel Lord ◽  
Jean-François Boucher
Keyword(s):  
Large Scale ◽  
Ad Hoc ◽  
Black Spruce ◽  
Tree Height ◽  
Jack Pine ◽  
Carbon Stocks ◽  
Allometric Equations ◽  
C Stocks ◽  
The Difference ◽  
Canadian Boreal Forest

Allometric equations use easily measurable biometric variables to determine the aboveground and belowground biomasses of trees. Equations produced for estimating the biomass within Canadian forests at a large scale have not yet been validated for eastern Canadian boreal open woodlands (OWs), where trees experience particular environmental conditions. In this study, we harvested 167 trees from seven boreal OWs in Quebec, Canada for biomass and allometric measurements. These data show that Canadian national equations accurately predict the whole aboveground biomass for both black spruce and jack pine trees, but underestimated branches biomass, possibly owing to a particular tree morphology in OWs relative to closed-canopy stands. We therefore developed ad hoc allometric equations based on three power models including diameter at breast height (DBH) alone or in combination with tree height (H) as allometric variables. Our results show that although the inclusion of H in the model yields better fits for most tree compartments in both species, the difference is minor and does not markedly affect biomass C stocks at the stand level. Using these newly developed equations, we found that carbon stocks in afforested OWs varied markedly among sites owing to differences in tree growth and species. Nine years after afforestation, jack pine plantations had accumulated about five times more carbon than black spruce plantations (0.14 vs. 0.80 t C·ha−1), highlighting the much larger potential of jack pine for OW afforestation projects in this environment.

scholarly journals An Integrated Credit-Based Incentive Protocol for Symbol-Level Network-Coded Cooperative Content Distribution among Vehicular Nodes

2018 ◽  
Vol 8 (11) ◽  
pp. 2035 ◽  
Author(s):  
Ing-Chau Chang ◽  
Chin-En Yen ◽  
Jacky Lo
Keyword(s):  
Ad Hoc ◽  
High Efficiency ◽  
Performance Metrics ◽  
Content Distribution ◽  
Long Latency ◽  
Distribution Process ◽  
Distribution Operations ◽  
The Difference ◽  
Different Content ◽  
Content Information

In traditional symbol-level network coding (SLNC)-based cooperative content distribution approaches, they ignore nodes in the vehicular ad hoc network (VANET) having various network-coded content pieces and distinct levels of interests and selfishness for different kinds of content data, which further prevents these vehicular nodes from forwarding their content information to other nodes. With these approaches, these nodes suffer from the low ratio and the long latency to receive all content information. In this paper, based on distinct levels of node interests and selfishness on different content information, we first categorize vehicular nodes into four classes, that is, the destination, intermediate, irrelevant and overhearing ones and then designate their associated credit-based incentive approaches. Second, we modify the flow of traditional SLNC-based cooperative content distribution operations and propose the content bitmap to realize the difference of network-coded content pieces among vehicular nodes. Further, we rigidly combine the proposed credit-based incentive approach with the modified SLNC-based cooperative content distribution operations in SocialCode to encourage all classes of vehicular nodes to rise their incentives for sharing content data in the cooperative content distribution process. Finally, we perform NS-2 simulations on a street map of downtown Taipei, Taiwan to exhibit the high efficiency of SocialCode over related credit-based incentive approaches by analyzing the following performance metrics, that is, average decoding percentage, file downloading delay and credits, with respect to different file sizes and total numbers of vehicular nodes. As the best knowledge we have, SocialCode is one of the first few researches that works on the integration between the credit-based incentive protocol and the SLNC-based cooperative content distribution.

Towards an Improved Parameter-Free Entrainment Model for Snow Avalanches

2021 ◽  
Author(s):  
Dieter Issler
Keyword(s):  
Snow Cover ◽  
Ad Hoc ◽  
Shear Stresses ◽  
Entrainment Rate ◽  
Snow Layer ◽  
Present Contribution ◽  
Weak Layer ◽  
Model Combining ◽  
The Difference ◽  
The 1960S

<p>On physical grounds, the rate of bed entrainment in gravity mass flows should be determined by the properties of the bed material and the dynamical variables of the flow. Due to the complexity of the process, most entrainment formulas proposed in the literature contain some ad-hoc parameter not tied to measurable snow properties. Among the very few models without free parameters are the Eglit–Grigorian–Yakimov (EGY) model of frontal entrainment from the 1960s and two formulas for basal entrainment, one from the 1970s due to Grigorian and Ostroumov (GO) and one (IJ) implemented in NGI’s flow code MoT-Voellmy. A common feature of these three approaches is their treating erosion as a shock and exploiting jump conditions for mass and momentum across the erosion front. The erosion or entrainment rate is determined by the difference between the avalanche-generated stress at the erosion front and the strength of the snow cover. The models differ with regard to how the shock is oriented and which momentum components are considered. The present contribution shows that each of the three models has some shortcomings: The EGY model is ambiguous if the avalanche pressure is too small to entrain the entire snow layer, the IJ model neglects normal stresses, and the GO model disregards shear stresses and acceleration of the eroded mass. As they stand, neither the GO nor the IJ model capture situations―observed experimentally by means of profiling radar―in which the snow cover is not eroded progressively but suddenly fails on a buried weak layer as the avalanche flows over it. We suggest a way to resolve the ambiguity in the EGY model and sketch a more comprehensive model combining all three approaches to capture gradual entrainment from the snow-cover surface together with erosion along a buried weak layer.</p>

Asynchronous quadratic control for constrained hidden markov jump linear systems with incomplete MTPM and MOCPM

2021 ◽  
Author(s):  
Jin Zhu ◽  
Kai Xia ◽  
Geir E Dullerud
Keyword(s):  
Linear Systems ◽  
Controller Design ◽  
Hidden Markov ◽  
Transition Probability ◽  
Original System ◽  
Transition Probability Matrix ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Weighting Matrix ◽  
Markov Jump Linear Systems

Abstract This paper investigates the quadratic optimal control problem for constrained Markov jump linear systems with incomplete mode transition probability matrix (MTPM). Considering original system mode is not accessible, observed mode is utilized for asynchronous controller design where mode observation conditional probability matrix (MOCPM), which characterizes the emission between original modes and observed modes is assumed to be partially known. An LMI optimization problem is formulated for such constrained hidden Markov jump linear systems with incomplete MTPM and MOCPM. Based on this, a feasible state-feedback controller can be designed with the application of free-connection weighting matrix method. The desired controller, dependent on observed mode, is an asynchronous one which can minimize the upper bound of quadratic cost and satisfy restrictions on system states and control variables. Furthermore, clustering observation where observed modes recast into several clusters, is explored for simplifying the computational complexity. Numerical examples are provided to illustrate the validity.

scholarly journals Reading the bed morphology of a mountain stream: a geomorphometric study on high-resolution topographic data

2010 ◽  
Vol 14 (2) ◽  
pp. 393-405 ◽  
Author(s):  
S. Trevisani ◽  
M. Cavalli ◽  
L. Marchi
Keyword(s):  
High Resolution ◽  
Ad Hoc ◽  
Flow Direction ◽  
Spatial Scales ◽  
Mountain Stream ◽  
Topographic Data ◽  
The Difference ◽  
Morphological Differences ◽  
High Level ◽  
Local Anomalies

Abstract. High-resolution topographic data expand the potential of quantitative analysis of the earth surface, improving the interpretation of geomorphic processes. In particular, the morphologies of the channel beds of mountain streams, which are characterised by strong spatial variability, can be analysed much more effectively with this type of data. In this study, we analysed the aerial LiDAR topographic data of a headwater stream, the Rio Cordon (watershed area: 5 km2), located in the Dolomites (north-eastern Italy). The morphology of the channel bed of Rio Cordon is characterised by alternating step pools, cascades, and rapids with steps. We analysed the streambed morphology by means of ad hoc developed morphometric indices, capable of highlighting morphological features at a high level of spatial resolution. To perform the analysis and the data interpolation, we carried out a channel-oriented coordinate transformation. In the new coordinate system, the calculation of morphometric indices in directions along and transverse to the flow direction is straightforward. Three geomorphometric indices were developed and applied as follows: a slope index computed on the whole width of the channel bed, directional variograms computed along the flow direction and perpendicular to it, and local anomalies, calculated as the difference between directional variograms at different spatial scales. Directional variograms in the flow direction and local anomalies have proven to be effective at recognising morphologic units, such as steps, pools and clusters of large boulders. At the spatial scale of channel reaches, these indices have demonstrated a satisfactory capability to outline patterns associated with boulder cascades and rapids with steps, whereas they did not clearly differentiate between morphologies with less marked morphological differences, such as step pools and cascades.

scholarly journals Ad hoc properties and locations in Maltese

2015 ◽  
Vol 1 ◽  
pp. 64-85 ◽  
Author(s):  
Gréte Dalmi
Keyword(s):  
Ad Hoc ◽  
Semantic Theory ◽  
Alternative States ◽  
Verbal Predicate ◽  
Spatio Temporal ◽  
The Difference ◽  
Copular Sentences ◽  
Event Variable ◽  
Temporal Variable ◽  
Account Variation

This paper aims to show that the four-way BE-system of Maltese can best be accommodated in a theory of non-verbal predication that builds on alternative states, without making any reference to the Davidsonian spatio-temporal event variable. The existing theories of non-verbal predicates put the burden of explaining the difference between the ad hoc vs. habitual interpretations either solely on the non-verbal predicate, by postulating an event variable in their lexical layer (see Kratzer 1995; Adger and Ramchand 2003; Magri 2009; Roy 2013), or solely on the copular or non-copular primary predicate, which contains an aspectual operator or an incorporated abstract preposition, responsible for such interpretive differences (Schmitt 2005, Schmitt and Miller 2007, Gallego and Uriagereka 2009, 2011, Marín 2010, Camacho 2012). The present proposal combines Maienborn’s (2003, 2005a,b, 2011) discourse-semantic theory of copular sentences with Richardson’s (2001, 2007) analysis of non-verbal adjunct predicates in Russian, based on alternative states. Under this combined account, variation between the ad hoc vs. habitual interpretations of non-verbal predicates is derived from the presence or absence of a modal OPalt operator that can bind the temporal variable of non-verbal predicates in accessible worlds, in the sense of Kratzer (1991). In the absence of this operator, the temporal variable is bound by the T0 head in the standard way. The proposal extends to non-verbal predicates in copular sentences as well as to argument and adjunct non-verbal predicates in non-copular sentences.

On Kierkegaard’s “The Difference between a Genius and an Apostle”

2019 ◽  
Vol 26 (3-4) ◽  
pp. 310-337
Author(s):  
Patrick Hart
Keyword(s):  
Ad Hoc ◽  
Early Christianity ◽  
Pauline Studies ◽  
The Difference

Abstract In “The Difference Between a Genius and an Apostle,” Kierkegaard deploys the figure of Paul as the archetype of an apostle, who “does not develop in such a way as he gradually becomes what he is [according to potentiality].” This claim would seem at odds with much contemporary Pauline scholarship, which understands Paul’s writings as an ad hoc, developing, quasi-guerrilla sort of theology. While this may be the case, Kierkegaard’s essay is nonetheless deserving of attention, for it highlights an issue that arguably remains a tacit foundation of Pauline studies – namely, the identification and resulting allure of Paul as an inherently authoritative figure in early Christianity.

Communiqué Issues in MANET and VANET Protocols With Network Security Disquiet

2020 ◽  
pp. 195-220 ◽  
Author(s):  
Mamata Rath ◽  
Bibudhendu Pati ◽  
Jhum Swain
Keyword(s):  
Ad Hoc Networks ◽  
Mobile Ad Hoc Networks ◽  
Network Topology ◽  
Mobile Networks ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Course Of Action ◽  
Mobile Stations ◽  
The Difference ◽  
Hoc Networks

With faster expansion of mobile networks and quicker increment of web clients, more individuals approach worldwide data and communication innovation, because of which the issues of utilizing web as a worldwide stage and empowering the savvy protests and machines to coordinate, discuss, register, and ascertain slowly develops. In mobile ad-hoc networks (MANETs) and vehicular ad-hoc networks (VANET), the mobile stations and vehicles are self-reconfigurable as per the difference in network topology. Joint action between convenient centers is more basic because of the way that they confront significant difficulties, for example, frailty to work securely while protecting its advantages and performing secure guiding among center points. In the presence of vindictive hubs, one of the rule challenges in MANET is to plot ground-breaking security course of action that can shield MANET from different routing assaults.

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