In this talk we will describe some early results on the problem of ambulance location in Tijuana. We will present optimal methods based on relaxations of integer programs and suboptimal approximate methods.

Mammary carcinoma is a common type of cancer that appears mostly in women under a certain age and can be inherited to future generations [2]. Biologist are exploring new treatments that can avoid the development of breast cancer in patients with hight risk of malignant cell mutations by experiment directly in mice. The genetically engineered mice (GEM) have proven extremely useful for studying breast cancer and have become the animal model for human breast cancer [2]. Studies in vivo are useful because represents real dynamics of the tumor cells in presence of immunotherapy for some complex types of cancer, Fomchenko et al.[3] have presented a model of brain tumors that can be applied in preclinical trials, Kwon et al.[4] presents a recent study of a possible model that describe the biological dynamics of the lung cancer by validating the results in mouse, Bianca et al.[6] presents the first nonlinear model of the carcinoma mammary cancer. Mathematical models are tools used in engineering and science to predict functional relationships between certain input and output variables. Mathematical modeling thus provide feedback to biologists on the suitability of experimental data, and they in turn can help improve and refinethe mathematical models. Thus the mathematical modeling provides the opportunity of improving both the understanding and prediction of biological phenomena [5].

Using the method of localization compact invariant sets (LOCI) [8] in biological models [9],[10], we define a region that contains the whole complex dynamics of the model where the upper bound represents the maximal concentration of population that can exist and also inside the region we can analyzed equilibrium points or define sufficient conditions of attractivity. In this paper is analyzed at the moment one case of study for the nonlinear tenth dimensional system describing the dynamics between the immune system and mammary carcinoma antigen by Bianca et al.[7], where the variables Xi2R5+;0;i= 1;2;5;8;9. The model is shown below:

The variable X1 represents the number of injected vaccine cells,X2 is the number of P-185 tumor associated antigens,X5the number of interleukin 12,X8is the number of cancer cells andX9the number of activated cytotoxic cells, the parameters are mention in [7] and all have positive values. In this case of study the vaccine can directly eradicate all the cancer cells and any antigen associate to the tumor due to the combination of cytotoxic cells and immunotherapy interleukin 12. Local stability is made by numerical simulation as well as finding equilibrium points. Has a result of this analysis we found four equilibrium points were three of them are negative equilibrium points. In this work are not consider the negative equilibrium points because they lack of biological sense, which leads to only one equilibrium point that is unique and locally stable. The Lyapunov function is shown below:

Upper bounds for each of the variable stated are presented. The intersection of all the upper bounds provides the localization domain of all compact invariant sets of the model.

For one case of study the model (1) which is a reduced dynamic model of Bianca [7] we present local stability by numerical simulation and using the Lyapunov function 2 we ensure global asymptotic stability of the equilibrium point. The upper bounds define the region that contains the dynamic of the model including the unique equilibrium point.

[1] Chávarri-Guerra, Y., Villarreal-Garza, C., Liedke,P. E., Knaul, F., Mohar, A., Finkelstein, D. M., Goss, P. E. “Breastcancer in Mexico: a growing challenge to health and the health system".The Lancet Oncology, 13(8), p. 335-343, 2012.

[2] Cardiff, R. D.,Kenney, N. “Mouse mammary tumor biology: a short history".Advances in cancer research, 98, p. 53-116,2007.

[3] Fomchenko, E. I., Holland, E. C.“Mouse models of brain tumors and their applications in preclinical trials".ClinicalCancer Research, 12(18), p. 5288-5297, 2006.

[4] Kwon, M. C., Berns, A. “Mouse models for lung cancer".Molecular oncology, 7(2), p. 165-177,2013.

[5] Klipp, E., Herwig, R., Kowald, A., Wierling, C., Lehrach, H.“Systems biology in practice: concepts, implementation andapplication". John Wiley & Sons , 2008.

[6] Bianca, C., Pennisi, M. “The triplex vaccine effects in mammary carcinoma: A nonlinear model in tune with SimTriplex".Nonlinear Analysis: Real World Applications, 13, p. 1913-1940, 2012.

[7] Bianca, C., Chiacchio, F., Pappalardo, F., Pennisi, M. “Mathematical modeling of the immune system recognition tomammary carcinoma antigen".BMC bioinformatics, 13(Suppl 17), S21, 2012.

[8] Krishchenko, A. P., Starkov, K. E. “Localization of compact invariant sets of the Lorenz system".Physics Letters A,353(5), p. 383-388, 2006.

[9] Starkov, K. E., Coria, L. N. “Global dynamics of the Kirschner,Panetta model for the tumor immunotherapy".NonlinearAnalysis: Real World Applications, 14(3), p. 1425-1433, 2013.

[10] Starkov, K. E., Gamboa, D. “Localization of compact invariant sets and global stability in analysis of one tumor growthmodel".Mathematical Methods in the Applied Sciences, 37(18), p. 2854-2863, 2014.

This work deals with the problem of the optimization of multiproduct batch plantdesign (MBPD) found in a biopharmaceutical manufacturing process. The aim of this work is to minimize the investment cost and find out the number and size of parallel equipment units in each stage. For this purpose, it is proposed to solve the problem in two different ways: the first way is by using particle swarm algorithms (PSA) and the second way is by genetic algorithms (GAs). This paper presents the effectiveness and performance comparison of PSA and GAs for optimal design of multiproduct batch plant.The calculation results (investment cost, number and size of equipment, computational time, CPU time and idle times in plant) obtained by GAs are better than PSA. This methodology can help the decision makers and constitutes a very promising framework forfinding asset of good solutions. Keywords: Biopharmaceutical manufacturing, mathematical modeling, particle swarm algorithms, genetic algorithms, batch plant design.

This work considers the ambulance location problem for the Red Cross in Tijuana, Baja California, Mex-ico. The solution to the ambulance location problem is to optimally locate all available ambulances withinthe city such that coverage of the city population is maximized and a quick response to any emergency isensured. The problem is posed using three different coverage models, these are: the Location Set CoveringModel (LSCM), Maximal Covering Location Problem (MCLP) and Double Standard Model (DSM). Usingreal-world data recovered from over 44 thousand emergency calls received by the Red Cross of Tijuana,several scenarios were generated that provide different perspectives of the demand throughout the city,considering such factors as the time of day, work and off-days, geographical organization and call priority.These models are solved using Integer Linear Programming, and solutions are compared with the current coverage provided by the Red Cross. Results show that coverage and response times can be substantially improved without additional resources.

One of the core problems for Emergency Medical Services (EMS) is the location problem of available ambulances [?]. The capability of these services to save lives depends greatly on the time it takes foran ambulance to arrive on the scene of an emergency. Hence, it is important to position all available ambulances in such a way that any emergencies that arise may be dealt with promptly.

The population in the city of Tijuana, Baja California, Mexico is approximately 1.6 million inhabitants [?].Currently, the Red Cross of Tijuana (RCT) has 11 ambulances in service and 8 bases, that cover about 98%of the medical emergencies throughout the city [?]. On average, there is one ambulance for every 145,000inhabitants. In 2013 the RCT provided EMS to 37,000 people. Average response time was approximately14 minutes with a standard deviation of 7 minutes. In 75% of all incidents the ambulance arrived within 18minutes and in 90% of all incidents it arrived within 23 minutes. In an emergency situation, the probabilitythat a patient survives depends on the time it takes for the ambulance to arrive, if response time was notquick enough the patient may suffer permanent injury. Therefore, it is very important to ensure that all emergencies can be responded to as fast as possible, by properly locating all available ambulances in the city.

To solve the ambulance location problem in Tijuana, three models are used in this work. These are theLocation Set Covering Model [?], Maximal Covering Location Problem[?] and Double Standard Model[?]. Using the LSCM, MCLP and DSM models, several scenarios were solved to determine the optimalambulance locations during different hours of the day and days of the week, in the city of Tijuana. Twosets of demand points were considered. The first is based on the locations of 92 neighborhoods and ismerely artificial while the second was created from EMS records from the Red Cross using clustering.Both sets offer different perspectives of the demand throughout the city. Accounting for the priority ofEMS requests, ambulance locations that favor demand points with higher priority requests were obtained.Generally speaking, solving all these scenarios with these three models has shown that demand coverage and response times can be improved with the resources currently available.

The LSCM experiments have shown that all demand could be covered using about half the number of ambulances currently in service, with a response time of 14 minutes. With the MCLP experiments, it has been shown that demand coverage, with a response time of 10 minutes, could be improved by as much as22% only by relocating the current 8 bases of the Red Cross. Also, almost all demand could be coveredby properly locating all 11 ambulances in service. As for the DSM experiments, with these 11 ambulancesit would be possible to cover all demand with a response time of 14 minutes, 95% of all demand within10 minutes and still provide double coverage to more than 85% of all demand. However, all of this istheoretical, and, in practice, real coverage and response times may vary, as they depend on many otherfactors beyond what has been considered in this work so far, such as time dependent travel times, weatherconditions, roadblocks, etc. Nonetheless, the results of this work may be used as tools to aid in the decision making about the location of ambulances in the city.

So far the ambulance location problem has been addressed, leaving the relocation problem to be solved.This arises when an ambulance is dispatched to the scene of an emergency and it becomes necessary torelocate one or more ambulances to maintain adequate coverage of the city population

The aging of the world population has lead to new health problems. People now live longer, but unfortunately the quality of life of the elderly is deplorable in many cases. The number of old people affected by brain disorders have increased significantly in recent years. Among these disorders, dementia, which has no cure, is one of the major health problems of the elderly.

Wandering and falls, which are closely related, are among the problems that most significantly affect patients with dementia. Wandering may lead to falls, and consequently, tosevere injuries. In fact, nearly one third of people over 75 years old suffer at least one fall every year. Also, falls are one of the main causes of death or severe injuries of people over 65 years old. This is the reason why people with dementia need constant supervision, and impose a heavy burden to families and caregivers. To alleviate this problem, the development of fall detection systems for the elderly is an important research topic[1].

In this paper, a non-invasive falls detection system for the elderly, based on the use of WSN, is proposed. The main objective of the system is to detect in real-time if someone has fallen, and to alert the caregivers to provide assistance. A rapid response may help to provide timely medical assistance, and prevent as much damage as possible.

The proposed system uses the acoustic signal sensed by the motes, as well as signal processing and pattern recognition techniques, to detect a fall. To illustrate this, Fig. 1 shows the block diagram for the proposed system.

Data sampling. The nodes of the WSN, placed at fixed locations (i.e., the room of the patient), are equipped with a microphone, and are constantly sensing the environment. When the intensity of the collected sound is larger than a threshold, the gathered data are sent to the sink. The sink uses these data as input of a signal-processing algorithm based on the use of cross-correlation. Since sampling rate is an important factor in pattern recognition, based on experimental results and to the to Nyquist theorem[2], a fixed sampling rate of 4 KHz was used.Cross-correlation (alignment). To avoid any missed event, sequences are aligned using a template as a reference, which was obtained using a real fall event. The cross-correlation of two time sequences measures the similarity between a sequence, and shifted similar sequences as a function of the lag. Features extraction. The MFCC have been widely used for speech/audio recognition [3], and represents the short-term power spectrum of a sound, based on a linear cosine transform of a log power spectrum on a nonlinear Mel scale of frequency. The MFCCs take into consideration human perception sensitivity with respect to frequencies.

Initially, the sampled data are stored in small frames of N samples, where the most used value for N is 256. The frames then must be converted from time domain to frequency domain, this is archived by the use of fast Fourier transform (FFT). A Mel filters bank will process the frequency domain data. In order to create the filter bank on Mel scale, a frequency conversion is needed. Eqn. 1 is used to compute the Mel scale convention, where M(f) is the frequency on Mel scale. A lower and an upper frequency cutoff are needed, where the upper frequency on the filter bank is limited to half the sampling rate frequency [4].

This is the process to convert the log Mel spectrum into time domain using discrete cosine transform (DCT). The result of the conversion is called Mel frequency cepstrum coefficient. The set of coefficient is called the acoustic vectors. Therefore, each input utterance is transformed into a sequence of acoustic vector. The output, after applying the DCT, is known as Mel frequency cepstrum coefficient.

Matching process. The DTW algorithm measures the similarity between two temporal sequences, and it is also used for speech recognition [5]. The DTW algorithm can calculate the optimal alienation path from two series or templates, representing the measured similarity with a coefficient called the total distance cost [6].The absolute distance between the values of twosequences is calculated using the Euclidean distance computation. Each matrix element (i, j) corresponds to the alignment between i and j. Eqn.2calculates the accumulated measured distance.

Finally, when the calculated total distance cost is less or equal than a given threshold, the system concludes that a fall has occurred. Otherwise, the system ignores the event. It is important to note that this threshold is obtained for the particular scenario where the system is used, considering the patient, the floor of the room, the ambient noise, among others.

Many health problems have increased as the world’s population ages. Among them, accidental falls are one of the main causes of injuries of the elderly. In this paper, a non-invasive falls detection system, based on the use of WSN, was proposed. If a fall is detected, an alert signal is sent to caregiver in order to provide timely medical assistance, and prevent as much damage as possible.

To validate the proposed system, we built a prototype and conducted a series of experiments. The obtained results from the experimental tests showed that the proposed system has a detection rate of 90%when no acoustic interference is present. Otherwise, the detection rate is nearly 80%.However, it can be improved adding more sensors, which may allow the detection of other important causes of injuries, such as wandering.

[1]N. Batsch and M. Mittelman, "World Alzheimer Report 2012: Overcoming the stigma of dementia," London: Alzheimer’s Disease International, vol. 75, 2012.

[2]R. K. Bansal, A. Goel, and M. K. Sharma, MATLAB and Its Applications in Engineering: Pearson Education, 2009.

[3]C. K. On, P. M. Pandiyan, S. Yaacob, and A. Saudi, "Mel-frequency cepstral coefficient analysis in speech recognition," in Computing & Informatics, 2006. ICOCI'06. International Conference on, 2006, pp. 1-5.

[4]S. Young, The HTK Book: Entropic Cambridge Research Laboratory, 1997.

[5]C. S. Myers, A Comparative Study of Several Dynamic Time Warping Algorithms for Speech Recognition: Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 1980.

[6]"Dynamic Time Warping," in Information Retrieval for Music and Motion, ed: Springer Berlin Heidelberg, 2007, pp. 69-84.