On critical cardinalities related to QQ-sets

In this note we collect some known information and prove new results about the small uncountable cardinal $\mathfrak q_0$. The cardinal $\mathfrak q_0$ is defined as the smallest cardinality $|A|$ of a subset $A\subset \mathbb R$ which is not a $Q$-set (a subspace $A\subset\mathbb R$ is called a $Q$-set if each subset $B\subset A$ is of type $F_\sigma$ in $A$). We present a simple proof of a folklore fact that $\mathfrak p\le\mathfrak q_0\le\min\{\mathfrak b,\mathrm{non}(\mathcal N),\log(\mathfrak c^+)\}$, and also establish the consistency of a number of strict inequalities between the cardinal $\mathfrak q_0$ and other standard small uncountable cardinals. This is done by combining some known forcing results. A new result of the paper is the consistency of $\mathfrak{p} < \mathfrak{lr} < \mathfrak{q}_0$, where $\mathfrak{lr}$ denotes the linear refinement number. Another new result is the upper bound $\mathfrak q_0\le\mathrm{non}(\mathcal I)$ holding for any $\mathfrak q_0$-flexible cccc $\sigma$-ideal $\mathcal I$ on $\mathbb R$.Comment: 8 page

Multifractal characteristics of external anal sphincter based on sEMG signals

This work presents the application of Multifractal Detrended Fluctuation Analysis for the surface electromyography signals obtained from the patients suffering from rectal cancer. The electrical activity of an external anal sphincter at different levels of medical treatment is considered. The results from standard MFDFA and the EMD--based MFDFA method are compared. Two distinct scaling regions were identified. Within the region of short time scales the calculated spectra exhibit the shift towards higher values of the singularity exponent for both methods. In addition obtained spectra are shifted towards the lower values of singularity exponent for the EMD--based MFDFA.Comment: 10 pages, 6 figures, 2 table

The distribution of information for sEMG signals in the rectal cancer treatment process

The electrical activity of external anal sphincter can be registered with surface electromyography. This signals are known to be highly complex and nonlinear. This work aims in characterisation of the information carried in the signals by harvesting the concept of information entropy. We will focus of two classical measures of the complexity. Firstly the Shannon entropy is addressed. It is related to the probability spectrum of the possible states. Secondly the Spectral entropy is described, as a simple frequency-domain analog of the time-domain Shannon characteristics. We discuss the power spectra for separate time scales and present the characteristics which can represent the dynamics of electrical activity of this specific muscle group. We find that the rest and maximum contraction states represent rather different spectral characteristic of entropy, with close-to-normal contraction and negatively skewed rest state.Comment: 6 pages, 5 figures, 1 tabl

Embedded Object Detection with Custom LittleNet, FINN and Vitis AI DCNN Accelerators

Object detection is an essential component of many systems used, for example, in advanced driver assistance systems (ADAS) or advanced video surveillance systems (AVSS). Currently, the highest detection accuracy is achieved by solutions using deep convolutional neural networks (DCNN). Unfortunately, these come at the cost of a high computational complexity; hence, the work on the widely understood acceleration of these algorithms is very important and timely. In this work, we compare three different DCNN hardware accelerator implementation methods: coarse-grained (a custom accelerator called LittleNet), fine-grained (FINN) and sequential (Vitis AI). We evaluate the approaches in terms of object detection accuracy, throughput and energy usage on the VOT and VTB datasets. We also present the limitations of each of the methods considered. We describe the whole process of DNNs implementation, including architecture design, training, quantisation and hardware implementation. We used two custom DNN architectures to obtain a higher accuracy, higher throughput and lower energy consumption. The first was implemented in SystemVerilog and the second with the FINN tool from AMD Xilinx. Next, both approaches were compared with the Vitis AI tool from AMD Xilinx. The final implementations were tested on the Avnet Ultra96-V2 development board with the Zynq UltraScale+ MPSoC ZCU3EG device. For two different DNNs architectures, we achieved a throughput of 196 fps for our custom accelerator and 111 fps for FINN. The same networks implemented with Vitis AI achieved 123.3 fps and 53.3 fps, respectively

Embedded Object Detection with Custom LittleNet, FINN and Vitis AI DCNN Accelerators

Object detection is an essential component of many systems used, for example, in advanced driver assistance systems (ADAS) or advanced video surveillance systems (AVSS). Currently, the highest detection accuracy is achieved by solutions using deep convolutional neural networks (DCNN). Unfortunately, these come at the cost of a high computational complexity; hence, the work on the widely understood acceleration of these algorithms is very important and timely. In this work, we compare three different DCNN hardware accelerator implementation methods: coarse-grained (a custom accelerator called LittleNet), fine-grained (FINN) and sequential (Vitis AI). We evaluate the approaches in terms of object detection accuracy, throughput and energy usage on the VOT and VTB datasets. We also present the limitations of each of the methods considered. We describe the whole process of DNNs implementation, including architecture design, training, quantisation and hardware implementation. We used two custom DNN architectures to obtain a higher accuracy, higher throughput and lower energy consumption. The first was implemented in SystemVerilog and the second with the FINN tool from AMD Xilinx. Next, both approaches were compared with the Vitis AI tool from AMD Xilinx. The final implementations were tested on the Avnet Ultra96-V2 development board with the Zynq UltraScale+ MPSoC ZCU3EG device. For two different DNNs architectures, we achieved a throughput of 196 fps for our custom accelerator and 111 fps for FINN. The same networks implemented with Vitis AI achieved 123.3 fps and 53.3 fps, respectively