text:
\section{Introduction}

	The worm Caenorhabditis elegans (C. elegans) is a model organism for neurobiology as it displays fairly sophisticated behavior despite having only 302 neurons. One such behavior of interest is chemotaxis: the ability to sense chemicals such as NaCl and to then move in response to the sensed concentration.
	The worm prefers certain concentrations of NaCl as it associates them with finding food, with these concentrations thus acting as setpoints for the worm.
	This ability to search for and follow the level set (which is an isocontour in 2D) for a particular setpoint concentration is called contour tracking, and has been observed experimentally in the worm \cite{luo2006sensorimotor}. Remarkably, the worm is able to track contours in a highly resource-constrained manner with just one concentration sensor and a small number of neurons. Contour tracking is also an important function for autonomously navigating robots, and it is thus of interest from an engineering standpoint to study the small yet efficient chemotaxis circuit of C. elegans. The emergence of energy-efficient nanoscale Neuromorphic hardware \cite{dutta2017leaky} motivates mapping these compact chemotaxis circuits onto Spiking Neural Networks (SNNs) in order to instantiate autonomously navigating robots operating under severe resource and energy constraints.

	One of the strategies that the worm uses is called klinokinesis, wherein the worm makes abrupt turns away from its current direction. Klinokinesis requires the worm to compare the current sensed concentration with past samples to estimate the concentration gradient along its path of motion. It turns away when it is above the setpoint and senses a positive gradient, or if it is below the setpoint and senses a negative gradient. It thus corrects its path so that it is always moving towards the setpoint.
	A model for the sensory neurons used to compute temporal derivatives was proposed in \cite{appleby2012model}.
	Santurkar and Rajendran added motor neurons to the model from \cite{appleby2012model} to propose an SNN for klinokinesis \cite{santurkar2015c}. They also demonstrated hardware compatibility with standard CMOS circuitry. However, their SNN required external currents to operate correctly and thus was not an autonomous solution. Shukla, Dutta and Ganguly resolved this problem by designing SNNs for the rate-coded logic operations required by the klinokinesis circuit and ensuring correctness of operation \cite{shukla2018design}. Furthermore, they incorporated an additional sub-circuit to allow the worm to escape local extrema, reduced the response latency of the SNN by incorporating anticipatory control and demonstrated feasibility on nanoscale neuromorphic hardware.

	An important limitation of klinokinesis is that it only uses the sign of the gradient and not its magnitude. Thus while klinokinesis ensures that the worm is always moving towards the setpoint, it does not ensure that it takes the shortest path. By definition, the direction with the highest gradient magnitude corresponds to the path of steepest ascent or descent. Indeed, the worm is known to align itself along (or against) the gradient via gradual turns in a process called klinotaxis. The worm performs klinotaxis by estimating the spatial gradient in the direction perpendicular to its current path by comparing concentration values to the left and right of its head while moving in a snake-like sinusoidal motion, using this estimate to gradually correct its path. Izquierdo and Lockery proposed a mechanistic model for gradient ascent using klinotaxis and learned model parameters via evolutionary algorithms \cite{izquierdo2010evolution}. Izquierdo and Beer subsequently attempted to map this model onto the connectome of the worm \cite{izquierdo2013connecting}.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=0.85\linewidth]{motiv.png}}
		\caption{(a) Timeline and comparison of this paper with past literature. (b) Gradient ascent to illustrate navigation mechanisms. Left: The bot makes abrupt turns to correct its path by using only the sign of the gradient, and thus takes a circuitous route to the peak. Center: The bot gradually corrects its path to align with the direction of steepest ascent and thus takes a much shorter route to the peak. Also note the sinusoidal motion of the bot. Right: This plot is only to visualize orthokinesis. Note that the arrows become denser close to the peak, depicting how the bot slows down near the setpoint and regions with large gradients.}
		\label{toon}
	\end{figure}

	The first important contribution of this paper is to build upon the gradient ascent circuit in \cite{izquierdo2010evolution} to develop a novel adaptive klinotaxis circuit that can be autonomously configured to perform gradient ascent, gradient descent, and disabled upon reaching the setpoint. Second, we implement this adaptive klinotaxis circuit with spiking neurons and then integrate it with the klinokinesis SNN from \cite{shukla2018design}. It is important to note that these strategies serve complementary roles, with klinokinesis allowing for rapid turns to ensure that the worm always moves closer to the setpoint, and klinotaxis allowing the worm to gradually optimize its path \cite{iino2009parallel,itskovits2018concerted}. Indeed, the worm is known to use klinokinesis and klinotaxis in tandem \cite{iino2009parallel}.
	However, in the context of contour tracking, it is important to understand how klinotaxis and klinokinesis can work together. In particular, the worm must align with the gradient until it reaches the setpoint and must subsequently move perpendicular to the gradient to follow the setpoint contour, thus requiring the worm to change its behavior based on how close it is to the setpoint. This problem was previously encountered in work by Skandari, Iino and Manton who proposed a non-adaptive, non-spiking model that attempts to extend Lockery's work to perform contour tracking \cite{skandari2016analogue}. Their simulations show that their network for reaching the setpoint and their network for subsequently following the contour are incompatible with each other, leading to a failure in tracking contours near regions with large gradients. The adaptive nature of our klinotaxis circuit allows us to address this important problem. Furthermore, the gradual nature of klinotaxis steering leads to large deviations from the setpoint while following the desired contour, a problem that we are able to address by also including the klinokinesis circuit to enable faster turns. Our circuit thus allows us to seamlessly integrate the benefits of both these navigation strategies.

	We also incorporate orthokinesis in our SNN model, wherein the bot can also regulate its speed as a function of sensed concentration \cite{benhamou1989animals}. This allows it to slow down near the setpoint and near regions with large gradients, leading to a further reduction in deviations from the setpoint while following the desired contour. To the best of our knowledge, this is the first circuit model that successfully integrates klinokinesis, klinotaxis and orthokinesis.

	\section{Proposed Algorithm}

	\subsection{Adaptive Klinotaxis}

	Klinotaxis is the mechanism whereby, as the worm moves along its sinusoidal trajectory, it compares the values of sensed concentrations in one half-cycle to those in the next half-cycle, and then changes its course based on this information. Klinotaxis has typically been studied in the context of gradient ascent, wherein the worm will bias its motion towards the side which is better aligned with the local gradient direction, thus gradually aligning with the gradient and performing steepest ascent, and thus allowing the worm to reach the peak faster. Crucially, if the worm had two spatially separated concentration sensors, then it could compare the values from these sensors to estimate the gradient direction, which is called tropotaxis. However, the worm only has one concentration sensor, thus requiring it to use its own body motion to sample to the left and right of its path, as it does with its sinusoidal motion. Such a setting is of great interest for highly resource constrained bots that are too small to carry two bulky sensors and where the spatial separation between sensors is too small to enable tropotaxis.
	In this paper, we enable our bot to not only perform gradient ascent, but also enable gradient descent and the ability to switch off the klinotaxis mechanism entirely. Furthermore, this change in behavior is affected autonomously based on sensed concentration, and we thus call this adaptive klinotaxis.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=0.7\linewidth]{network.png}}
		\caption{Block Diagram for the full network.}
		\label{net}
	\end{figure}

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{klinotax.png}}
		\caption{(a) Network diagram for the gradient detector and klinotaxis blocks. The gradient detector functions by computing a temporal estimate for the gradient: $C(t) - C_{avg}(t)$, which is normalized by $C_{avg}(t)$ to make this estimate scale-invariant. It is further divided by $v(t)$ to convert the temporal derivative to a spatial derivative ($\frac{\mathrm{d} C}{\mathrm{d} t} = v(t) \cdot \frac{\mathrm{d} C}{\mathrm{d}x}$). This spatial derivative is then rate-coded using two sparsely firing leaky-integrate-and-fire neurons, with the refractory periods acting as saturating non-linearity. (b) Signal flow through the klinotaxis block. The bias shifts the piecewise linear sigmoidal response curve to the left or right, while the sum of currents from the oscillator and gradient detector, $I^{\pm}_{ph}(t)$, is the input to these shifted response curves. For $b=0.0$: The positive parts of the input are retained and thus the turning rate increases with $I_g(t)$. Thus the bot turns slower when aligned against the gradient - gradient descent. For $b=0.5$: Both the positive and negative parts of the input are retained and the effect of $I_g(t)$ is cancelled out. Thus the bot's turning rate is independent of the gradient - klinotaxis disabled. For $b=1.0$: Effectively, the negative parts of the input are retained and thus the turning rate decreases with $I_g(t)$. Thus the bot turns slower when aligned along the gradient - gradient ascent.}
		\label{taxnet}
	\end{figure}

	The gradient detector and klinotaxis blocks are depicted in Fig. \ref{taxnet}(a). Like the worm, our bot has a single concentration sensor whose output at time $t$ is the sensed concentration $C(t)$. This $C(t)$ is used to compute an adaptive difference-estimate for the gradient, $I_{ad}(t)$, given as:

	\begin{equation}
	I_{ad}(t) = \frac{C(t) - C_{avg}(t)}{C_{avg}(t) \cdot v(t)} \\
	\end{equation}

	Here $C_{avg}(t)$ is the sensed concentration averaged over the past $10$ seconds, and thus $C(t) - C_{avg}(t)$ is an estimate for the temporal derivative $\frac{\mathrm{d} C}{\mathrm{d} t}$. This is dynamically scaled by $\frac{1}{C_{avg}(t)}$ to allow the gradient detector neurons to effectively utilize available signaling bandwidth and to make its response invariant to the average concentration, allowing our bot to operate in environments where the concentrations can vary over many orders of magnitude. This is thus a simple but important modification to the static scaling used in \cite{santurkar2015c,shukla2018design,izquierdo2010evolution,izquierdo2013connecting}. This is in turn scaled by $\frac{1}{v(t)}$ to convert the temporal derivative to a spatial derivative, in line with $\frac{\mathrm{d} C}{\mathrm{d} x} = \frac{1}{v(t)} \cdot \frac{\mathrm{d} C}{\mathrm{d} t}$. This requires the existence of a feedback loop which gives the sensory neurons access to the bot's velocity, as depicted in Fig. \ref{net}.
	Note that such divisive gain modulation has also been observed in neurons in-vivo \cite{bastian1986gain,vestergaard2015divisive}.
	Also note that while operating with a constant speed, as was the case in \cite{santurkar2015c,shukla2018design}, the temporal and spatial gradients are linearly proportional to each other and thus there was no need for such speed-dependent scaling in past work.

	The positive and negative parts of this signal given are respectively denoted by $I^+_{ad}(t) = I_{ad}(t) \cdot \delta(I_{ad}(t) > 0) ~;~ I^-_{ad}(t) = I_{ad}(t) \cdot \delta(I_{ad}(t) < 0)$, where $\delta(.)$ is a delta-function which is $1$ if the input condition is true and is $0$ otherwise. Next, $I^+_{ad}(t)$ and $I^-_{ad}(t)$ are respectively fed into neurons $N_+$ and $N_-$, noting that $I_{ad}(t)$ was encoded this way using two neurons because neurons can only have positive firing rates. We model $N_+$ and $N_-$ as leaky integrate-and-fire (LIF) neurons with respective membrane potentials $V_+$ and $V_-$ which evolve as:

	\begin{equation}
	C_G\frac{\mathrm{d} V_+}{\mathrm{d} t} = I^+_{ad}(t) - \frac{V_+(t)}{R_G} ~;~
	C_G\frac{\mathrm{d} V_-}{\mathrm{d} t} = I^-_{ad}(t) - \frac{V_-(t)}{R_G}
	\end{equation}

	Here $C_G$ and $R_G$ are respectively the membrane capacitance and resistance. The neurons $N_+$ and $N_-$ fire when $V_+$ and $V_-$ respectively cross the firing threshold $V_T$, and the membrane voltage is then reset to $0$ for the duration of the refractory period.
	The spike-trains of $N_+$ and $N_-$ are convolved with the kernel $\kappa(t) = e^{\frac{-t}{\tau_1}} - e^{\frac{-t}{\tau_2}} ~;~ \tau_1 > \tau_2$ to generate the respective output currents $I_g^+(t)$ and $I_g^-(t)$.
	This is an instance of rate-coding wherein $I_g^{\pm}(t)$ increases with $I^{\pm}_{ad}(t)$. However this mapping is non-linear due to the refractory period, and crucially, $I_g^{\pm}(t)$ saturates for large values of $I^{\pm}_{ad}(t)$.
	The refractory period and parameters of $\kappa(t)$ are chosen so that this maximum value of $I_g^{\pm}(t)$ is $1$, a fact that will be used in the klinotaxis circuit.
	Apart from this non-linear response, the other advantage of using spiking neurons is that unlike analog neurons they are not always on and are thus much more energy-efficient.
	Finallly, the rate-coded gradient estimate is given as $I_g(t) = I_g^+(t) - I_g^-(t)$.

	Having discussed the gradient detector circuit, we now proceed to describe the klinotaxis circuit.
	The first component is the oscillator current $I_{osc}(t)$ with time period $T_{osc}$, which is used to generate two oscillatory signals with opposite phases as: $I^+_{osc}(t) = I_{osc}(t)$ and $I^-_{osc}(t) = -I_{osc}(t)$. The second component is the bias function which determines the mode of operation of the klinotaxis circuit and is denoted by $b(t)$. The third input, $I_g(t)$, comes from the gradient detector discussed above.
	Output from these three blocks is fed to the two non-linear ``phase'' blocks, denoted by ``Phase($\pm$)'' in Fig. \ref{taxnet}. These phase blocks are the most important part of the circuit, yielding output currents $I^{\pm}_{ph}(t)$. The net turning rate $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t}$ due to klinotaxis is given by the scaled difference in output of these two phase blocks, where $\theta(t)$ is the bot's steering angle. We choose the convention wherein a positive change in $\theta$ will correspond to turning clockwise.

	\begin{align}
	I_{osc}(t) &= I^+_{osc}(t) = - I^-_{osc}(t) = \sin(\frac{2\pi t}{T_{osc}}) \\
	b(t) &=
	\begin{aligned}
	\left\{\begin{matrix}
	1.0 ~;~ &(C_T - C(t)) > \varepsilon \\
	0.5 ~;~ &|C(t) - C_T| < \varepsilon \\
	0.0 ~;~ &(C(t) - C_T) > \varepsilon
	\end{matrix}\right.
	\end{aligned}\\
	I_g(t) &= I_g^+(t) - I_g^-(t) \\
	I^{\pm}_{ph}(t) &= \sigma(\alpha \cdot I^{\pm}_{osc}(t) + \beta \cdot I_g(t) + b(t))  \\
	\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} &= w_m \cdot (I^{+}_{ph}(t) - I^{-}_{ph}(t))
	\end{align}

	To understand (4), observe that if we wish to reach the setpoint concentration $C_T$ to within an tolerance $\varepsilon$, it is straightforward to see that we want $b(t) = 1.0$ (gradient ascent) for $C(t) < (C_T - \varepsilon)$, $b(t) = 0.0$ for $C(t) > (C_T + \varepsilon)$ (gradient descent), and $b(t) = 0.5$ (disable klinotaxis) for $\left | C(t) - C_T \right | < \varepsilon$. By disabling klinotaxis close to the setpoint, we allow klinokinesis to seamlessly take over, allowing the bot to follow the setpoint contour using klinokinesis as demonstrated in \cite{shukla2018design}. These mechanisms thus serve complementary roles, with klinotaxis used to reach the setpoint, and klinokinesis to subsequently follow the setpoint contour. In (6), the non-linear response of the phase blocks, $\sigma(x)$ (for input $x$), is equal to $0$ for $x < 0$, $x$ for $0<x<1$, and $1$ for $x>1$. Thus it increases linearly between $0$ and $1$ and saturates outside this range. While we have used this piecewise-linear form for $\sigma(x)$ in subsequent analysis, we have used a smoother and more biologically feasible approximation in our final contour tracking simulations, given as $\sigma(x) \approx 0.5 \cdot (1 + \tanh(2 \cdot x - 1))$.
	Also note that $\alpha$, $\beta$ and $w_M$ are positive scaling constants.

	We now proceed to describe the adaptive klinotaxis mechanism for the half-cycle from $0$ to $T_{osc} / 2$. We will first do this for $b = 1.0$, corresponding to gradient ascent. In this half-cycle $I^+_{osc}(t)$ is positive and thus $\sigma(1 + \alpha \cdot I^+_{osc}(t)) = 1$, meaning that $I^{+}_{ph}(t)$ saturates to $1$. On the other hand, as $I^-_{osc}(t)$ is negative during this cycle, $\sigma(1 + \alpha \cdot I^-_{osc}(t)) = 1 + \alpha \cdot I^-_{osc}(t)$ and thus $I^{-}_{ph}(t)$ lies in the linear region. Note that these are approximate statements that ignore the contribution from $I_g(t)$. While it can be verified that these statements are exact for $\frac{T_{osc}}{2 \pi} sin^{-1}(\frac{\beta}{\alpha}) < t < \frac{T_{osc}}{2}$ (by noting that both $I_g(t)$ and $I_{osc}(t)$ have maximum amplitude of $1$), they will be assumed for the entire half-cycle for ease of analysis. We are thus interpreting $\beta \cdot I_g(t)$ as a small perturbation to the output. We then have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = 1 - (1 + \alpha \cdot I^-_{osc}(t) + \beta \cdot I_g(t)) = \alpha \cdot (-I^-_{osc}(t)) - \beta \cdot I_g(t) = \alpha \cdot I_{osc}(t) - \beta \cdot I_g(t)$.
	Thus we see that for $b=1.0$ the bot turns slower when aligned along the gradient ($I_g(t) > 0$) and turns faster when aligned against the gradient ($I_g(t)< 0$). The bot's net motion is thus biased and it tends to align along the gradient, thus performing gradient ascent. This is depicted in Fig. \ref{taxmech}(c) wherein the turning rate is higher and lower respectively for the red part ($I_g(t)<0$) and green part ($I_g(t)>0$) of the trajectories.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{mech.png}}
		\caption{(a) Path of the bot over five oscillator cycles for the three choices of $b$. Note how the trajectory bends towards, does not bend, and bends away from the steepest gradient direction respectively for $b = \{1.0, 0.5, 0.0\}$. (b) Timeplots for system variables over a represenative cycle, one for each choice of $b$. The top plot shows that the rate-coding estimate is indeed able to follow the true gradient. The middle plot shows the difference in clipping of left ($I^{+}_{ph}(t)$) and right ($I^{-}_{ph}(t)$) motor neurons, for choices of $b$. The bottom plot shows how the gradient changes the turning rate vis-a-vis the zero-gradient case. Note that there is no skew for $b=0.5$, while the skews for $b=0.0$ and $b=1.0$ are precisely opposite to one another.
			(c) Trajectory of the bot performing gradient ascent for a half-cycle, with and without klinotaxis enabled. Top: The bot is initially aligned against the gradient and is turning clockwise. Bottom: The bot is initially aligned along the gradient and is turning anticlockwise. The green and red parts of the curves respectively correspond to sensing positive and negative gradients, making the bot turn slower and faster respectively. In both cases the axis of motion is initially perpendicular to the gradient and at the end of the half-cycle this axis has rotated clockwise towards the gradient direction when klinotaxis is enabled.}
		\label{taxmech}
	\end{figure}

	Next, we consider gradient descent with $b=0.0$. In the first half-cycle $I^-_{osc}(t)$ is negative and thus $\sigma(0 + \alpha \cdot I^-_{osc}(t)) = 0$, and thus $I^{-}_{ph}(t)$ saturates to $0$. On the other hand, as $I^+_{osc}(t)$ is positive during this cycle, $\sigma(0 + \alpha \cdot I^+_{osc}(t)) = \alpha \cdot I^+_{osc}(t)$ and thus $I^{+}_{ph}(t)$ lies in the linear region. Again, treating $\beta \cdot I_g(t)$ as a perturbation that only affects the non-saturated phase, we have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = (\alpha \cdot I^+_{osc}(t) + \beta \cdot I_g(t)) - 0 = \alpha \cdot I_{osc}(t) + \beta \cdot I_g(t)$. Thus we see that for $b=0.0$ the bot turns faster when aligned along the gradient ($I_g(t) > 0$) and turns slower when aligned against the gradient ($I_g(t)< 0$). The bot's net motion is thus biased and it tends to align against the gradient, thus performing gradient descent.

	Finally, we discuss the case of disabling klinotaxis by setting $b=0.5$. Furthermore, we choose hitherto unspecified constants as $\alpha = 0.4$ and $\beta = 0.1$. For all time $t$ we then have that $\left | 0.1 \cdot I_g(t) \pm 0.4 \cdot I_{osc}(t) + 0.5 \right | < 0.1 + 0.4 + 0.5 = 1$, recalling that by design, both $I_g(t)$ and $I_{osc}(t)$ have a maximum magnitude of $1$. Thus for $b=0.5$, neither $I^{+}_{ph}(t)$ nor $I^{-}_{ph}(t)$ saturate and both lie in the linear region. We then have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = (\alpha \cdot I^+_{osc}(t) + \beta \cdot I_g(t) + 0.5) - (\alpha \cdot I^-_{osc}(t) + \beta \cdot I_g(t) + 0.5) = \alpha \cdot (I^+_{osc}(t) - I^-_{osc}(t))  = 2\alpha \cdot I_{osc}(t)$.
	Thus in this case, $I_g(t)$ has no effect on the turning rate of the bot and hence the klinotaxis mechanism stands disabled.
	We note that the amplitudes of $\alpha = 0.4$ and $\beta = 0.1$ respectively for the oscillatory and gradient terms were chosen such that they sum up to $0.5$. This was done to maximize the dynamic range of input in the linear output regime, while also not allowing this input to saturate. Also note that the larger value of $0.4$ was chosen for the oscillatory component to ensure that the bot swerves to the left and right with a large enough amplitude and thus samples it local environment, despite the modulatory effect of the gradient term. At the same time, the amplitude of $0.1$ for the gradient term is large enough to ensure that it does have a sufficiently large modulatory effect to enable klinotaxis. In summary, the turning rate in the first half-cycle is given as:

	\begin{equation}
	\frac{\mathrm{d} \theta}{\mathrm{d} t} = \left\{\begin{matrix}
	w_M \cdot \left (\alpha \cdot I_{osc}(t) + \beta \cdot I_{grad}(t) \right ) ~;~ b = 0.0 \\ w_M \cdot 2\alpha \cdot I_{osc}(t) ~;~ b = 0.5 \\
	w_M \cdot \left (\alpha \cdot I_{osc}(t) - \beta \cdot I_{grad}(t) \right ) ~;~ b = 1.0
	\end{matrix}\right.
	\end{equation}

	It can be verified that in the next half-cycle from $T_{osc} / 2$ to $T_{osc}$, we get the same expression for $\frac{\mathrm{d} \theta}{\mathrm{d} t}$ as given in (8), but now with a negative sign.
	Thus the bot turns clockwise in one half-cycle and anti-clockwise in the next. Note also that it suffices to describe one full-cycle as the same mechanism recurs over time.

	\subsection{Klinokinesis}

	Klinokinesis is a course correction algorithm, wherein the worm turns around when it senses that it is moving away from the desired setpoint concentration. This happens in two cases: when it senses $\frac{\mathrm{d} C(t)}{\mathrm{d} t} > 0, ~ C(t) > C_T$ or if $\frac{\mathrm{d} C(t)}{\mathrm{d} t} < 0, ~ C(t) < C_T$.
	Note that this requires computing an AND operation over the sensed gradient and concentration values for which we use the SNN developed in \cite{shukla2018design}. While klinokinesis allows for rapid corrections to the bot's path and is thus well suited to closely following the contour once it is reached, it is not capable of finding the shortest path to the setpoint as it only uses the sign of the gradient and does not seek out the direction of \emph{steepest} descent, thus motivating the inclusion of the complementary mechanism of klinotaxis.

	\subsection{Orthokinesis}

	We incorporate orthokinesis to reduce overshoot whilst following the setpoint contour using klinokinesis. We describe the bot's speed in discrete-time for ease of understanding, while noting that it is straightforward to convert this to continuous-time. For discrete time $1, ..., t-1, t, ...$, the bot speed is given as:

	\begin{equation}
	v[t] = v_c + \frac{k \cdot v[t-1] \cdot \left | C[t] - C_T \right |}{a + \left | \frac{\mathrm{d} C[t-1]}{\mathrm{d} x} \right |}
	\end{equation}

	Here $v_c$ is a constant that ensures that the worm continues to move along the setpoint contour despite the second term going to $0$ close to $C_T$. Furthermore, the second term is proportional to $v[t-1]$ as a means of enforcing continuity in the values of $v[t]$. The term $\left | C[t] - C_T \right |$ is included so that the worm slows down close to the setpoint. Thus by allowing the worm to slow down near the setpoint concentration, we enable improved contour tracking. We would also like the bot to slow down near regions with high gradient magnitudes so that it does not overshoot the setpoint. This is ensured by including $\frac{\mathrm{d} C[t-1]}{\mathrm{d} x}$ in the denominator, which is the output of the gradient detector in the previous time step. Finally, $k$ is a constant scaling factor while $a$ is a constant that ensures that the denominator is never $0$.

	\section{Results and Conclusions}

	The algorithms are visually compared in Fig.\ref{comp}(a). Note that the bot was started from the same starting point and initial angle in all three plots. Using only klinokinesis (left), the bot takes a long route to reach the setpoint and exhibits large overshoots around the setpoint contour. Adding klinotaxis (middle) allows the bot to reach the setpoint using a much faster route while also reducing setpoint deviation. Adding orthokinesis (right) further reduces the setpoint deviation.

	We now define the Time to Reach Ratio (TRR) of an algorithm $A$ for a setpoint $C_T$ as the time taken to first reach $C_T$ using $A$ divided by the time to first reach $C_T$ using klinokinesis. Clearly, the TRR also depends on the particular concentration landscape, starting point and initial angle. Here we consider the aggregated TRR obtained by averaging the TRR over 10 landscapes, 10 starting points for each landscape and 10 initial angles for each tuple of landscape and starting point. Also note that the TRR for klinokinesis will trivially be $1.0$.
	The second metric is adopted from \cite{santurkar2015c,shukla2018design} to quantify the deviation from the setpoint once the bot has reached the contour. This metric is the average deviation ratio from setpoint (ADR), defined as $ADR = \frac{1}{T - T_0} \int_{T_0}^{T}\frac{\left | C(t) - C_T \right|}{C_{max} - C_{min}}dt$, where $T_0$ is the first time that the bot reaches $C_T$, $T$ is the total simulation time, $C_{max}$ and $C_{min}$ are respectively the maximum and minimum concentrations values on the landscape. Thus the ADR measures the time-averaged ratio of the absolute deviation to the landscape concentration range. We report the aggregated ADR by averaging over the same set of configurations as for the aggregrated TRR.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{compare.png}}
		\caption{(a) The dotted line in all three contour tracking plots is the setpoint contour corresponding to $C_T = 55mM$. (b) Left: Benchmarking with TRR and ADR. Right: Impact on ADR of dividing by $C_{avg}(t)$ while computing the gradient estimate.}
		\label{comp}
	\end{figure}

	The algorithms are benchmarked using these two metrics in the left panel of Fig. \ref{comp}(b). We find that there is a drastic reduction in the TRR, by a factor of 2.6, due to the inclusion of klinotaxis, implying that the bot reaches the setpoint faster.
	Remarkably this improvement is achieved despite the bot's effective speed being reduced by a factor of roughly 7.5 by moving along a sinusoidal path instead of a straight line. As expected, a second effect of this reduced effective velocity is that the inclusion of klinotaxis also reduces the ADR, by a significant factor of 3.8.
	The TRR is slightly larger with the inclusion of orthokinesis as the bot slows down near the setpoint. However we observe a larger reduction in ADR, demonstrating that orthokinesis can adaptively trade-off speed for a significant reduction in setpoint overshoot. The TRR and ADR respectively reduced by a factor of 2.4 and 8.7 by including both klinotaxis and orthokinesis (w.r.t just klinokinesis). Also note that the standard deviation of the TRR for both the ``klinokinesis + klinotaxis'' and ``klinokinesis + klinotaxis + orthokinesis'' algorithms were found to be $0.05$. The standard deviation of the ADR for ``klinokinesis only'', ``klinokinesis + klinotaxis'' and ``klinokinesis + klinotaxis + orthokinesis'' algorithms were respectively found to be $0.34$, $0.08$ and $0.04$.

	In the right panel of Fig.\ref{comp}(b), we quantitatively demonstrate the drastic improvement in robustness of chemotaxis due to the inclusion of $C_{avg}(t)$ in the denominator of (1). We plot the ADR for the ``klinokinesis + klinotaxis + orthokinesis'' algorithm as a function of average landscape concentration. Without adaptive scaling (red), the ADR is comparable to that with adaptive scaling (green) in a narrow range of average concentration, but degrades rapidly away from this optimal range. Similar plots were also obtained for the ``klinokinesis only'' and ``klinokinesis + klinotaxis'' algorithms.
	This shows that previously proposed chemotaxis algorithms in the literature (that did not incorporate dynamic scaling) are not robust to concenctration rescaling, highlighting the importance of the novel dynamic scaling proposed in this paper. Finally, we refer the reader to \cite{santurkar2015c} for a demonstration of the SNN-based klinokinesis-only strategy achieving lower ADR compared to PID control while also being significantly more energy efficient, with these results holding transitively for the schemes proposed here.

	In conclusion, we have presented a scale-invariant, adaptive chemotaxis algorithm using spiking neurons that successfully combines klinotaxis, klinokinesis and orthokinesis. This allows us to perform robust, resource constrained and energy efficient contour tracking while achieving state-of-the-art performance.

	\bibliographystyle{splncs04}

\section{Introduction}

	The worm Caenorhabditis elegans (C. elegans) is a model organism for neurobiology as it displays fairly sophisticated behavior despite having only 302 neurons. One such behavior of interest is chemotaxis: the ability to sense chemicals such as NaCl and to then move in response to the sensed concentration.
	The worm prefers certain concentrations of NaCl as it associates them with finding food, with these concentrations thus acting as setpoints for the worm.
	This ability to search for and follow the level set (which is an isocontour in 2D) for a particular setpoint concentration is called contour tracking, and has been observed experimentally in the worm \cite{luo2006sensorimotor}. Remarkably, the worm is able to track contours in a highly resource-constrained manner with just one concentration sensor and a small number of neurons. Contour tracking is also an important function for autonomously navigating robots, and it is thus of interest from an engineering standpoint to study the small yet efficient chemotaxis circuit of C. elegans. The emergence of energy-efficient nanoscale Neuromorphic hardware \cite{dutta2017leaky} motivates mapping these compact chemotaxis circuits onto Spiking Neural Networks (SNNs) in order to instantiate autonomously navigating robots operating under severe resource and energy constraints.

	One of the strategies that the worm uses is called klinokinesis, wherein the worm makes abrupt turns away from its current direction. Klinokinesis requires the worm to compare the current sensed concentration with past samples to estimate the concentration gradient along its path of motion. It turns away when it is above the setpoint and senses a positive gradient, or if it is below the setpoint and senses a negative gradient. It thus corrects its path so that it is always moving towards the setpoint.
	A model for the sensory neurons used to compute temporal derivatives was proposed in \cite{appleby2012model}.
	Santurkar and Rajendran added motor neurons to the model from \cite{appleby2012model} to propose an SNN for klinokinesis \cite{santurkar2015c}. They also demonstrated hardware compatibility with standard CMOS circuitry. However, their SNN required external currents to operate correctly and thus was not an autonomous solution. Shukla, Dutta and Ganguly resolved this problem by designing SNNs for the rate-coded logic operations required by the klinokinesis circuit and ensuring correctness of operation \cite{shukla2018design}. Furthermore, they incorporated an additional sub-circuit to allow the worm to escape local extrema, reduced the response latency of the SNN by incorporating anticipatory control and demonstrated feasibility on nanoscale neuromorphic hardware.

	An important limitation of klinokinesis is that it only uses the sign of the gradient and not its magnitude. Thus while klinokinesis ensures that the worm is always moving towards the setpoint, it does not ensure that it takes the shortest path. By definition, the direction with the highest gradient magnitude corresponds to the path of steepest ascent or descent. Indeed, the worm is known to align itself along (or against) the gradient via gradual turns in a process called klinotaxis. The worm performs klinotaxis by estimating the spatial gradient in the direction perpendicular to its current path by comparing concentration values to the left and right of its head while moving in a snake-like sinusoidal motion, using this estimate to gradually correct its path. Izquierdo and Lockery proposed a mechanistic model for gradient ascent using klinotaxis and learned model parameters via evolutionary algorithms \cite{izquierdo2010evolution}. Izquierdo and Beer subsequently attempted to map this model onto the connectome of the worm \cite{izquierdo2013connecting}.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=0.85\linewidth]{motiv.png}}
		\caption{(a) Timeline and comparison of this paper with past literature. (b) Gradient ascent to illustrate navigation mechanisms. Left: The bot makes abrupt turns to correct its path by using only the sign of the gradient, and thus takes a circuitous route to the peak. Center: The bot gradually corrects its path to align with the direction of steepest ascent and thus takes a much shorter route to the peak. Also note the sinusoidal motion of the bot. Right: This plot is only to visualize orthokinesis. Note that the arrows become denser close to the peak, depicting how the bot slows down near the setpoint and regions with large gradients.}
		\label{toon}
	\end{figure}

	The first important contribution of this paper is to build upon the gradient ascent circuit in \cite{izquierdo2010evolution} to develop a novel adaptive klinotaxis circuit that can be autonomously configured to perform gradient ascent, gradient descent, and disabled upon reaching the setpoint. Second, we implement this adaptive klinotaxis circuit with spiking neurons and then integrate it with the klinokinesis SNN from \cite{shukla2018design}. It is important to note that these strategies serve complementary roles, with klinokinesis allowing for rapid turns to ensure that the worm always moves closer to the setpoint, and klinotaxis allowing the worm to gradually optimize its path \cite{iino2009parallel,itskovits2018concerted}. Indeed, the worm is known to use klinokinesis and klinotaxis in tandem \cite{iino2009parallel}.
	However, in the context of contour tracking, it is important to understand how klinotaxis and klinokinesis can work together. In particular, the worm must align with the gradient until it reaches the setpoint and must subsequently move perpendicular to the gradient to follow the setpoint contour, thus requiring the worm to change its behavior based on how close it is to the setpoint. This problem was previously encountered in work by Skandari, Iino and Manton who proposed a non-adaptive, non-spiking model that attempts to extend Lockery's work to perform contour tracking \cite{skandari2016analogue}. Their simulations show that their network for reaching the setpoint and their network for subsequently following the contour are incompatible with each other, leading to a failure in tracking contours near regions with large gradients. The adaptive nature of our klinotaxis circuit allows us to address this important problem. Furthermore, the gradual nature of klinotaxis steering leads to large deviations from the setpoint while following the desired contour, a problem that we are able to address by also including the klinokinesis circuit to enable faster turns. Our circuit thus allows us to seamlessly integrate the benefits of both these navigation strategies.

	We also incorporate orthokinesis in our SNN model, wherein the bot can also regulate its speed as a function of sensed concentration \cite{benhamou1989animals}. This allows it to slow down near the setpoint and near regions with large gradients, leading to a further reduction in deviations from the setpoint while following the desired contour. To the best of our knowledge, this is the first circuit model that successfully integrates klinokinesis, klinotaxis and orthokinesis.

	\section{Proposed Algorithm}

	\subsection{Adaptive Klinotaxis}

	Klinotaxis is the mechanism whereby, as the worm moves along its sinusoidal trajectory, it compares the values of sensed concentrations in one half-cycle to those in the next half-cycle, and then changes its course based on this information. Klinotaxis has typically been studied in the context of gradient ascent, wherein the worm will bias its motion towards the side which is better aligned with the local gradient direction, thus gradually aligning with the gradient and performing steepest ascent, and thus allowing the worm to reach the peak faster. Crucially, if the worm had two spatially separated concentration sensors, then it could compare the values from these sensors to estimate the gradient direction, which is called tropotaxis. However, the worm only has one concentration sensor, thus requiring it to use its own body motion to sample to the left and right of its path, as it does with its sinusoidal motion. Such a setting is of great interest for highly resource constrained bots that are too small to carry two bulky sensors and where the spatial separation between sensors is too small to enable tropotaxis.
	In this paper, we enable our bot to not only perform gradient ascent, but also enable gradient descent and the ability to switch off the klinotaxis mechanism entirely. Furthermore, this change in behavior is affected autonomously based on sensed concentration, and we thus call this adaptive klinotaxis.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=0.7\linewidth]{network.png}}
		\caption{Block Diagram for the full network.}
		\label{net}
	\end{figure}

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{klinotax.png}}
		\caption{(a) Network diagram for the gradient detector and klinotaxis blocks. The gradient detector functions by computing a temporal estimate for the gradient: $C(t) - C_{avg}(t)$, which is normalized by $C_{avg}(t)$ to make this estimate scale-invariant. It is further divided by $v(t)$ to convert the temporal derivative to a spatial derivative ($\frac{\mathrm{d} C}{\mathrm{d} t} = v(t) \cdot \frac{\mathrm{d} C}{\mathrm{d}x}$). This spatial derivative is then rate-coded using two sparsely firing leaky-integrate-and-fire neurons, with the refractory periods acting as saturating non-linearity. (b) Signal flow through the klinotaxis block. The bias shifts the piecewise linear sigmoidal response curve to the left or right, while the sum of currents from the oscillator and gradient detector, $I^{\pm}_{ph}(t)$, is the input to these shifted response curves. For $b=0.0$: The positive parts of the input are retained and thus the turning rate increases with $I_g(t)$. Thus the bot turns slower when aligned against the gradient - gradient descent. For $b=0.5$: Both the positive and negative parts of the input are retained and the effect of $I_g(t)$ is cancelled out. Thus the bot's turning rate is independent of the gradient - klinotaxis disabled. For $b=1.0$: Effectively, the negative parts of the input are retained and thus the turning rate decreases with $I_g(t)$. Thus the bot turns slower when aligned along the gradient - gradient ascent.}
		\label{taxnet}
	\end{figure}

	The gradient detector and klinotaxis blocks are depicted in Fig. \ref{taxnet}(a). Like the worm, our bot has a single concentration sensor whose output at time $t$ is the sensed concentration $C(t)$. This $C(t)$ is used to compute an adaptive difference-estimate for the gradient, $I_{ad}(t)$, given as:

	\begin{equation}
	I_{ad}(t) = \frac{C(t) - C_{avg}(t)}{C_{avg}(t) \cdot v(t)} \\
	\end{equation}

	Here $C_{avg}(t)$ is the sensed concentration averaged over the past $10$ seconds, and thus $C(t) - C_{avg}(t)$ is an estimate for the temporal derivative $\frac{\mathrm{d} C}{\mathrm{d} t}$. This is dynamically scaled by $\frac{1}{C_{avg}(t)}$ to allow the gradient detector neurons to effectively utilize available signaling bandwidth and to make its response invariant to the average concentration, allowing our bot to operate in environments where the concentrations can vary over many orders of magnitude. This is thus a simple but important modification to the static scaling used in \cite{santurkar2015c,shukla2018design,izquierdo2010evolution,izquierdo2013connecting}. This is in turn scaled by $\frac{1}{v(t)}$ to convert the temporal derivative to a spatial derivative, in line with $\frac{\mathrm{d} C}{\mathrm{d} x} = \frac{1}{v(t)} \cdot \frac{\mathrm{d} C}{\mathrm{d} t}$. This requires the existence of a feedback loop which gives the sensory neurons access to the bot's velocity, as depicted in Fig. \ref{net}.
	Note that such divisive gain modulation has also been observed in neurons in-vivo \cite{bastian1986gain,vestergaard2015divisive}.
	Also note that while operating with a constant speed, as was the case in \cite{santurkar2015c,shukla2018design}, the temporal and spatial gradients are linearly proportional to each other and thus there was no need for such speed-dependent scaling in past work.

	The positive and negative parts of this signal given are respectively denoted by $I^+_{ad}(t) = I_{ad}(t) \cdot \delta(I_{ad}(t) > 0) ~;~ I^-_{ad}(t) = I_{ad}(t) \cdot \delta(I_{ad}(t) < 0)$, where $\delta(.)$ is a delta-function which is $1$ if the input condition is true and is $0$ otherwise. Next, $I^+_{ad}(t)$ and $I^-_{ad}(t)$ are respectively fed into neurons $N_+$ and $N_-$, noting that $I_{ad}(t)$ was encoded this way using two neurons because neurons can only have positive firing rates. We model $N_+$ and $N_-$ as leaky integrate-and-fire (LIF) neurons with respective membrane potentials $V_+$ and $V_-$ which evolve as:

	\begin{equation}
	C_G\frac{\mathrm{d} V_+}{\mathrm{d} t} = I^+_{ad}(t) - \frac{V_+(t)}{R_G} ~;~
	C_G\frac{\mathrm{d} V_-}{\mathrm{d} t} = I^-_{ad}(t) - \frac{V_-(t)}{R_G}
	\end{equation}

	Here $C_G$ and $R_G$ are respectively the membrane capacitance and resistance. The neurons $N_+$ and $N_-$ fire when $V_+$ and $V_-$ respectively cross the firing threshold $V_T$, and the membrane voltage is then reset to $0$ for the duration of the refractory period.
	The spike-trains of $N_+$ and $N_-$ are convolved with the kernel $\kappa(t) = e^{\frac{-t}{\tau_1}} - e^{\frac{-t}{\tau_2}} ~;~ \tau_1 > \tau_2$ to generate the respective output currents $I_g^+(t)$ and $I_g^-(t)$.
	This is an instance of rate-coding wherein $I_g^{\pm}(t)$ increases with $I^{\pm}_{ad}(t)$. However this mapping is non-linear due to the refractory period, and crucially, $I_g^{\pm}(t)$ saturates for large values of $I^{\pm}_{ad}(t)$.
	The refractory period and parameters of $\kappa(t)$ are chosen so that this maximum value of $I_g^{\pm}(t)$ is $1$, a fact that will be used in the klinotaxis circuit.
	Apart from this non-linear response, the other advantage of using spiking neurons is that unlike analog neurons they are not always on and are thus much more energy-efficient.
	Finallly, the rate-coded gradient estimate is given as $I_g(t) = I_g^+(t) - I_g^-(t)$.

	Having discussed the gradient detector circuit, we now proceed to describe the klinotaxis circuit.
	The first component is the oscillator current $I_{osc}(t)$ with time period $T_{osc}$, which is used to generate two oscillatory signals with opposite phases as: $I^+_{osc}(t) = I_{osc}(t)$ and $I^-_{osc}(t) = -I_{osc}(t)$. The second component is the bias function which determines the mode of operation of the klinotaxis circuit and is denoted by $b(t)$. The third input, $I_g(t)$, comes from the gradient detector discussed above.
	Output from these three blocks is fed to the two non-linear ``phase'' blocks, denoted by ``Phase($\pm$)'' in Fig. \ref{taxnet}. These phase blocks are the most important part of the circuit, yielding output currents $I^{\pm}_{ph}(t)$. The net turning rate $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t}$ due to klinotaxis is given by the scaled difference in output of these two phase blocks, where $\theta(t)$ is the bot's steering angle. We choose the convention wherein a positive change in $\theta$ will correspond to turning clockwise.

	\begin{align}
	I_{osc}(t) &= I^+_{osc}(t) = - I^-_{osc}(t) = \sin(\frac{2\pi t}{T_{osc}}) \\
	b(t) &=
	\begin{aligned}
	\left\{\begin{matrix}
	1.0 ~;~ &(C_T - C(t)) > \varepsilon \\
	0.5 ~;~ &|C(t) - C_T| < \varepsilon \\
	0.0 ~;~ &(C(t) - C_T) > \varepsilon
	\end{matrix}\right.
	\end{aligned}\\
	I_g(t) &= I_g^+(t) - I_g^-(t) \\
	I^{\pm}_{ph}(t) &= \sigma(\alpha \cdot I^{\pm}_{osc}(t) + \beta \cdot I_g(t) + b(t))  \\
	\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} &= w_m \cdot (I^{+}_{ph}(t) - I^{-}_{ph}(t))
	\end{align}

	To understand (4), observe that if we wish to reach the setpoint concentration $C_T$ to within an tolerance $\varepsilon$, it is straightforward to see that we want $b(t) = 1.0$ (gradient ascent) for $C(t) < (C_T - \varepsilon)$, $b(t) = 0.0$ for $C(t) > (C_T + \varepsilon)$ (gradient descent), and $b(t) = 0.5$ (disable klinotaxis) for $\left | C(t) - C_T \right | < \varepsilon$. By disabling klinotaxis close to the setpoint, we allow klinokinesis to seamlessly take over, allowing the bot to follow the setpoint contour using klinokinesis as demonstrated in \cite{shukla2018design}. These mechanisms thus serve complementary roles, with klinotaxis used to reach the setpoint, and klinokinesis to subsequently follow the setpoint contour. In (6), the non-linear response of the phase blocks, $\sigma(x)$ (for input $x$), is equal to $0$ for $x < 0$, $x$ for $0<x<1$, and $1$ for $x>1$. Thus it increases linearly between $0$ and $1$ and saturates outside this range. While we have used this piecewise-linear form for $\sigma(x)$ in subsequent analysis, we have used a smoother and more biologically feasible approximation in our final contour tracking simulations, given as $\sigma(x) \approx 0.5 \cdot (1 + \tanh(2 \cdot x - 1))$.
	Also note that $\alpha$, $\beta$ and $w_M$ are positive scaling constants.

	We now proceed to describe the adaptive klinotaxis mechanism for the half-cycle from $0$ to $T_{osc} / 2$. We will first do this for $b = 1.0$, corresponding to gradient ascent. In this half-cycle $I^+_{osc}(t)$ is positive and thus $\sigma(1 + \alpha \cdot I^+_{osc}(t)) = 1$, meaning that $I^{+}_{ph}(t)$ saturates to $1$. On the other hand, as $I^-_{osc}(t)$ is negative during this cycle, $\sigma(1 + \alpha \cdot I^-_{osc}(t)) = 1 + \alpha \cdot I^-_{osc}(t)$ and thus $I^{-}_{ph}(t)$ lies in the linear region. Note that these are approximate statements that ignore the contribution from $I_g(t)$. While it can be verified that these statements are exact for $\frac{T_{osc}}{2 \pi} sin^{-1}(\frac{\beta}{\alpha}) < t < \frac{T_{osc}}{2}$ (by noting that both $I_g(t)$ and $I_{osc}(t)$ have maximum amplitude of $1$), they will be assumed for the entire half-cycle for ease of analysis. We are thus interpreting $\beta \cdot I_g(t)$ as a small perturbation to the output. We then have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = 1 - (1 + \alpha \cdot I^-_{osc}(t) + \beta \cdot I_g(t)) = \alpha \cdot (-I^-_{osc}(t)) - \beta \cdot I_g(t) = \alpha \cdot I_{osc}(t) - \beta \cdot I_g(t)$.
	Thus we see that for $b=1.0$ the bot turns slower when aligned along the gradient ($I_g(t) > 0$) and turns faster when aligned against the gradient ($I_g(t)< 0$). The bot's net motion is thus biased and it tends to align along the gradient, thus performing gradient ascent. This is depicted in Fig. \ref{taxmech}(c) wherein the turning rate is higher and lower respectively for the red part ($I_g(t)<0$) and green part ($I_g(t)>0$) of the trajectories.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{mech.png}}
		\caption{(a) Path of the bot over five oscillator cycles for the three choices of $b$. Note how the trajectory bends towards, does not bend, and bends away from the steepest gradient direction respectively for $b = \{1.0, 0.5, 0.0\}$. (b) Timeplots for system variables over a represenative cycle, one for each choice of $b$. The top plot shows that the rate-coding estimate is indeed able to follow the true gradient. The middle plot shows the difference in clipping of left ($I^{+}_{ph}(t)$) and right ($I^{-}_{ph}(t)$) motor neurons, for choices of $b$. The bottom plot shows how the gradient changes the turning rate vis-a-vis the zero-gradient case. Note that there is no skew for $b=0.5$, while the skews for $b=0.0$ and $b=1.0$ are precisely opposite to one another.
			(c) Trajectory of the bot performing gradient ascent for a half-cycle, with and without klinotaxis enabled. Top: The bot is initially aligned against the gradient and is turning clockwise. Bottom: The bot is initially aligned along the gradient and is turning anticlockwise. The green and red parts of the curves respectively correspond to sensing positive and negative gradients, making the bot turn slower and faster respectively. In both cases the axis of motion is initially perpendicular to the gradient and at the end of the half-cycle this axis has rotated clockwise towards the gradient direction when klinotaxis is enabled.}
		\label{taxmech}
	\end{figure}

	Next, we consider gradient descent with $b=0.0$. In the first half-cycle $I^-_{osc}(t)$ is negative and thus $\sigma(0 + \alpha \cdot I^-_{osc}(t)) = 0$, and thus $I^{-}_{ph}(t)$ saturates to $0$. On the other hand, as $I^+_{osc}(t)$ is positive during this cycle, $\sigma(0 + \alpha \cdot I^+_{osc}(t)) = \alpha \cdot I^+_{osc}(t)$ and thus $I^{+}_{ph}(t)$ lies in the linear region. Again, treating $\beta \cdot I_g(t)$ as a perturbation that only affects the non-saturated phase, we have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = (\alpha \cdot I^+_{osc}(t) + \beta \cdot I_g(t)) - 0 = \alpha \cdot I_{osc}(t) + \beta \cdot I_g(t)$. Thus we see that for $b=0.0$ the bot turns faster when aligned along the gradient ($I_g(t) > 0$) and turns slower when aligned against the gradient ($I_g(t)< 0$). The bot's net motion is thus biased and it tends to align against the gradient, thus performing gradient descent.

	Finally, we discuss the case of disabling klinotaxis by setting $b=0.5$. Furthermore, we choose hitherto unspecified constants as $\alpha = 0.4$ and $\beta = 0.1$. For all time $t$ we then have that $\left | 0.1 \cdot I_g(t) \pm 0.4 \cdot I_{osc}(t) + 0.5 \right | < 0.1 + 0.4 + 0.5 = 1$, recalling that by design, both $I_g(t)$ and $I_{osc}(t)$ have a maximum magnitude of $1$. Thus for $b=0.5$, neither $I^{+}_{ph}(t)$ nor $I^{-}_{ph}(t)$ saturate and both lie in the linear region. We then have $\frac{\mathrm{d} \theta(t)}{\mathrm{d} t} = (\alpha \cdot I^+_{osc}(t) + \beta \cdot I_g(t) + 0.5) - (\alpha \cdot I^-_{osc}(t) + \beta \cdot I_g(t) + 0.5) = \alpha \cdot (I^+_{osc}(t) - I^-_{osc}(t))  = 2\alpha \cdot I_{osc}(t)$.
	Thus in this case, $I_g(t)$ has no effect on the turning rate of the bot and hence the klinotaxis mechanism stands disabled.
	We note that the amplitudes of $\alpha = 0.4$ and $\beta = 0.1$ respectively for the oscillatory and gradient terms were chosen such that they sum up to $0.5$. This was done to maximize the dynamic range of input in the linear output regime, while also not allowing this input to saturate. Also note that the larger value of $0.4$ was chosen for the oscillatory component to ensure that the bot swerves to the left and right with a large enough amplitude and thus samples it local environment, despite the modulatory effect of the gradient term. At the same time, the amplitude of $0.1$ for the gradient term is large enough to ensure that it does have a sufficiently large modulatory effect to enable klinotaxis. In summary, the turning rate in the first half-cycle is given as:

	\begin{equation}
	\frac{\mathrm{d} \theta}{\mathrm{d} t} = \left\{\begin{matrix}
	w_M \cdot \left (\alpha \cdot I_{osc}(t) + \beta \cdot I_{grad}(t) \right ) ~;~ b = 0.0 \\ w_M \cdot 2\alpha \cdot I_{osc}(t) ~;~ b = 0.5 \\
	w_M \cdot \left (\alpha \cdot I_{osc}(t) - \beta \cdot I_{grad}(t) \right ) ~;~ b = 1.0
	\end{matrix}\right.
	\end{equation}

	It can be verified that in the next half-cycle from $T_{osc} / 2$ to $T_{osc}$, we get the same expression for $\frac{\mathrm{d} \theta}{\mathrm{d} t}$ as given in (8), but now with a negative sign.
	Thus the bot turns clockwise in one half-cycle and anti-clockwise in the next. Note also that it suffices to describe one full-cycle as the same mechanism recurs over time.

	\subsection{Klinokinesis}

	Klinokinesis is a course correction algorithm, wherein the worm turns around when it senses that it is moving away from the desired setpoint concentration. This happens in two cases: when it senses $\frac{\mathrm{d} C(t)}{\mathrm{d} t} > 0, ~ C(t) > C_T$ or if $\frac{\mathrm{d} C(t)}{\mathrm{d} t} < 0, ~ C(t) < C_T$.
	Note that this requires computing an AND operation over the sensed gradient and concentration values for which we use the SNN developed in \cite{shukla2018design}. While klinokinesis allows for rapid corrections to the bot's path and is thus well suited to closely following the contour once it is reached, it is not capable of finding the shortest path to the setpoint as it only uses the sign of the gradient and does not seek out the direction of \emph{steepest} descent, thus motivating the inclusion of the complementary mechanism of klinotaxis.

	\subsection{Orthokinesis}

	We incorporate orthokinesis to reduce overshoot whilst following the setpoint contour using klinokinesis. We describe the bot's speed in discrete-time for ease of understanding, while noting that it is straightforward to convert this to continuous-time. For discrete time $1, ..., t-1, t, ...$, the bot speed is given as:

	\begin{equation}
	v[t] = v_c + \frac{k \cdot v[t-1] \cdot \left | C[t] - C_T \right |}{a + \left | \frac{\mathrm{d} C[t-1]}{\mathrm{d} x} \right |}
	\end{equation}

	Here $v_c$ is a constant that ensures that the worm continues to move along the setpoint contour despite the second term going to $0$ close to $C_T$. Furthermore, the second term is proportional to $v[t-1]$ as a means of enforcing continuity in the values of $v[t]$. The term $\left | C[t] - C_T \right |$ is included so that the worm slows down close to the setpoint. Thus by allowing the worm to slow down near the setpoint concentration, we enable improved contour tracking. We would also like the bot to slow down near regions with high gradient magnitudes so that it does not overshoot the setpoint. This is ensured by including $\frac{\mathrm{d} C[t-1]}{\mathrm{d} x}$ in the denominator, which is the output of the gradient detector in the previous time step. Finally, $k$ is a constant scaling factor while $a$ is a constant that ensures that the denominator is never $0$.

	\section{Results and Conclusions}

	The algorithms are visually compared in Fig.\ref{comp}(a). Note that the bot was started from the same starting point and initial angle in all three plots. Using only klinokinesis (left), the bot takes a long route to reach the setpoint and exhibits large overshoots around the setpoint contour. Adding klinotaxis (middle) allows the bot to reach the setpoint using a much faster route while also reducing setpoint deviation. Adding orthokinesis (right) further reduces the setpoint deviation.

	We now define the Time to Reach Ratio (TRR) of an algorithm $A$ for a setpoint $C_T$ as the time taken to first reach $C_T$ using $A$ divided by the time to first reach $C_T$ using klinokinesis. Clearly, the TRR also depends on the particular concentration landscape, starting point and initial angle. Here we consider the aggregated TRR obtained by averaging the TRR over 10 landscapes, 10 starting points for each landscape and 10 initial angles for each tuple of landscape and starting point. Also note that the TRR for klinokinesis will trivially be $1.0$.
	The second metric is adopted from \cite{santurkar2015c,shukla2018design} to quantify the deviation from the setpoint once the bot has reached the contour. This metric is the average deviation ratio from setpoint (ADR), defined as $ADR = \frac{1}{T - T_0} \int_{T_0}^{T}\frac{\left | C(t) - C_T \right|}{C_{max} - C_{min}}dt$, where $T_0$ is the first time that the bot reaches $C_T$, $T$ is the total simulation time, $C_{max}$ and $C_{min}$ are respectively the maximum and minimum concentrations values on the landscape. Thus the ADR measures the time-averaged ratio of the absolute deviation to the landscape concentration range. We report the aggregated ADR by averaging over the same set of configurations as for the aggregrated TRR.

	\begin{figure}[htbp]
		\centerline{\includegraphics[width=\linewidth]{compare.png}}
		\caption{(a) The dotted line in all three contour tracking plots is the setpoint contour corresponding to $C_T = 55mM$. (b) Left: Benchmarking with TRR and ADR. Right: Impact on ADR of dividing by $C_{avg}(t)$ while computing the gradient estimate.}
		\label{comp}
	\end{figure}

	The algorithms are benchmarked using these two metrics in the left panel of Fig. \ref{comp}(b). We find that there is a drastic reduction in the TRR, by a factor of 2.6, due to the inclusion of klinotaxis, implying that the bot reaches the setpoint faster.
	Remarkably this improvement is achieved despite the bot's effective speed being reduced by a factor of roughly 7.5 by moving along a sinusoidal path instead of a straight line. As expected, a second effect of this reduced effective velocity is that the inclusion of klinotaxis also reduces the ADR, by a significant factor of 3.8.
	The TRR is slightly larger with the inclusion of orthokinesis as the bot slows down near the setpoint. However we observe a larger reduction in ADR, demonstrating that orthokinesis can adaptively trade-off speed for a significant reduction in setpoint overshoot. The TRR and ADR respectively reduced by a factor of 2.4 and 8.7 by including both klinotaxis and orthokinesis (w.r.t just klinokinesis). Also note that the standard deviation of the TRR for both the ``klinokinesis + klinotaxis'' and ``klinokinesis + klinotaxis + orthokinesis'' algorithms were found to be $0.05$. The standard deviation of the ADR for ``klinokinesis only'', ``klinokinesis + klinotaxis'' and ``klinokinesis + klinotaxis + orthokinesis'' algorithms were respectively found to be $0.34$, $0.08$ and $0.04$.

	In the right panel of Fig.\ref{comp}(b), we quantitatively demonstrate the drastic improvement in robustness of chemotaxis due to the inclusion of $C_{avg}(t)$ in the denominator of (1). We plot the ADR for the ``klinokinesis + klinotaxis + orthokinesis'' algorithm as a function of average landscape concentration. Without adaptive scaling (red), the ADR is comparable to that with adaptive scaling (green) in a narrow range of average concentration, but degrades rapidly away from this optimal range. Similar plots were also obtained for the ``klinokinesis only'' and ``klinokinesis + klinotaxis'' algorithms.
	This shows that previously proposed chemotaxis algorithms in the literature (that did not incorporate dynamic scaling) are not robust to concenctration rescaling, highlighting the importance of the novel dynamic scaling proposed in this paper. Finally, we refer the reader to \cite{santurkar2015c} for a demonstration of the SNN-based klinokinesis-only strategy achieving lower ADR compared to PID control while also being significantly more energy efficient, with these results holding transitively for the schemes proposed here.

	In conclusion, we have presented a scale-invariant, adaptive chemotaxis algorithm using spiking neurons that successfully combines klinotaxis, klinokinesis and orthokinesis. This allows us to perform robust, resource constrained and energy efficient contour tracking while achieving state-of-the-art performance.

	\bibliographystyle{splncs04}


Ok, so it wasn't "The Last Exorcism" after all. Here's "Part II: The Second Coming," an 88 bore without the nervy, shaky-camera found-footage conceit, without the doubting exorcist's moment of truth, without the chills of demonic possession thrills that the low-budget original film served up.
"Part II" is every bit as cheap and far more generic, nothing more than a run of the mill ghost story masquerading as The Devil Made Her Do It.
But she's seeing her dead daddy (Louis Herthum). she's hearing voices.
"Last Exorcism II" is a slower than slow thriller built around Bell, who isn't at her most subtle or empathetic here. There's fear and the burden of "If he seduces you, all hope is lost." Not that Bell as Nell gets that across. There's no urgency to the performance, or that of anybody else trying to save poor Nell from Hell.
It's a film of cheap shriek scares and fizzing frights that pack no punch. The usual tropes of these movies show up — exorcists who have the tools, but face personal demons, bleeding walls, birds that fly into a house where Nell hides out (Hey, it was ALIENS who caused that in "Dark Skies").
The effects are skimpy and cheesy, with that crazy contortion business that "Last Exorcist" took to new extremes rarely used.
Filmmaker Ed Gass-Donnelly sets too much of the action in broad daylight, which isn't spooky. The dull acting doesn't hide that there's not enough story to justify setting this in Voodooville, USA — New Orleans.
So one can only hope that when the say "Last Exorcism" this time, that they mean it.
Credits: Directed by Ed Gass-Donnelly, written by Damien Chazelle and Ed Gass-Donnelly. A CBS Films release.


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AL BENN
'Tabling' the good things
Alvin Benn
SELMA – With Passover well under way, we tend to think back to the days when our family managed to observe, as best we could, the religious tenets of our heritage. Raised in an Orthodox home instilled in me and my three siblings the love of traditional Jewish values even though, as the years passed, the four of us may have missed a beat or two when it came to holidays and observances.
That meant a week-long consumption of a bland, tasteless, hard to swallow cardboard-like substance known as matzo, matza or matzah depending on one's spelling preferences.
Eating matzo for eight days means "tabling" all the good things we loved to eat such as cookies, cakes, hot dogs, pizza and other delicious forms of pasta.
The first of the major Jewish holidays mentioned in the Bible, Passover is said to be observed by more Jews than any of the others except for Rosh Hashanah (the Jewish New Year) and Yom Kippur, (the Day of Atonement.)
Times have changed through the decades and many offspring of traditional Jewish families have opted for more comfortable religious lifestyles.
My sister Eileen Kranzel and her family attend a Reconstructionist synagogue in Mechanicsburg, Pa., just outside Harrisburg, Pennsylvania's Capital City. Reconstruction Judaism is relatively new and the Kranzels have become important members of their congregation.
It's tough to be Jewish in the Deep South and still follow "old country" traditions when there are no delis and kosher food markets on every street corner as is the case in some New York City neighborhoods.
"Passover in 2016 isn't the same as it was in the 1950s when we were growing up, but, what is?" Eileen said a few days ago when we chatted about "Pesach," a Hebrew word meaning the same thing.
The Benn family attended Congregation Degel Israel, an Orthodox synagogue, in Lancaster, Pa. So did almost every other family in the neighborhoods surrounding it.
The second floor of our butcher shop across the street from the synagogue was also the location of our Hebrew School. We attended three days a week after secular school and, naturally, didn't want to go, but our fathers "suggested" we be there or else.
It was led by an "old country" cantor who tried to teach us Hebrew as chickens were being slaughtered and made kosher on the first floor just below our desks.
The final cackling of chickens merged with the cantor's efforts to teach us the Hebrew alphabet. It was quite a mixture. All the boys wanted to do was get outside to play baseball.
As we grew up some of us grew apart from those traditions. Our bar mitzvahs not only signaled adulthood when we reached the age of 13, but also admission to a world far removed from synagogues in eastern Europe, the setting for that fictional, but amazingly accurate movie "Fiddler on the Roof."
Memories linger, however, and I haven't forgotten the image of my mother down on her hands and knees searching for any crumbs that might have eluded her eagle eyes during her quest for chametz – a Hebrew word for biblically forbidden foods during the week-long Passover holiday.
My grandfather was known to correct the rabbi in his readings of the Torah during services. One thing he'd always do, too, was politely reject our mother's invitation to eat with us. He was never quite sure if his youngest daughter kept kosher as it should be kept. She did, but he wasn't going to tempt fate.
I think he may have spied a tiny crumb, an almost invisible piece of chametz, lurking under the kitchen table.
To make sure we all stuck by the rules and regulations of keeping Passover as perfect as possible, even outside our house, my mother made matzo sandwiches for us to take to school.
Asked by my classmates just what that odd looking, less than appetizing "bread" was with tuna fish smeared inside, I offered to break off a little piece for them to sample. I'd have offered them the whole thing, but can't recall anybody ever taking up the offer.
With my birthday falling during the last week of April, I was well aware that I wouldn't be getting a birthday cake because they tend to have enough forbidden ingredients, especially chametz, to bring back memories of that old cantor from the "Old Country."
So, here I am, another birthday has arrived. It's today and, once again, I won't be getting a birthday cake, not even the tiniest nibble from a chocolate Moon Pie.
Passover: A time of joy

redpajama_set_name: RedPajamaCommonCrawl


The Kid Who Would Be King is a modern adaptation of the King Arthur legend, but does Joe Cornish's movie have an end-credits scene teasing a sequel? The tale of King Arthur and the Knights of the Round Table has been told and retold throughout the centuries, in various forms of media from film and TV to books and video games. While many retellings stick to the story's medieval setting, The Kid Who Would Be King brings King Arthur into the 21st Century - sort of.
Cornish's movie follows young Alexander Elliot (Louis Ashbourne Serkis), an ordinary boy who is regularly picked on at school along with his best friend Bedders (Dean Chaumoo). However, his life is changed when he stumbles upon King Arthur's sword, Excalibur, in a cement block on a construction site. The wizard Merlin (Patrick Stewart/Angus Imrie) arrives and attempts to help Alex assemble his own team of knights in order to battle Arthur's half-sister Morgana (Rebecca Ferguson), who had been imprisoned in hell by Arthur when the legendary king reigned. Still, it remains to be seen if Alex and his friends will be able to overcome their differences and defeat Morgana.
Now that The Kid Who Would Be King is hitting theaters, viewers may be wondering if there are any extra scenes or fun stingers after the credits. Unfortunately, The Kid Who Would Be King does NOT have a post-credits scene. So, while viewers can watch the credits to get an idea of all the people involved in the making of the film, moviegoers shouldn't expect anything extra at the very end.
The Kid Who Would Be King marks Cornish's first return to directing a feature-length film since his 2011 sci-fi movie Attack the Block, which starred a pre-Star Wars John Boyega. The inventive alien invasion flick was praised at the time by critics and fans, but ended up earning only $5 million at the box office. Still, Attack the Block and Cornish won a number of awards and accolades, and the movie remains a favorite among viewers to this day. Now, Cornish returns with a more family-friendly adventure in The Kid Who Would Be King, though it features many of the same markers of a Cornish film.
Considering the box office of Attack the Block, it seems likely The Kid Who Would Be King will be more of a financial success, if only because it's getting a wide release rather than a limited run. That said, it remains to be seen if the movie will be successful enough to prompt sequel talks. The Kid Who Would Be King's ending doesn't include an obvious sequel setup, but given the various characters from Arthurian legend who don't appear in the movie, there's certainly room for a follow-up. However, while viewers may hope to see The Kid Who Would Be King get a sequel, moviegoers should be aware the film doesn't include a post-credits scene setting up a sequel or offering any additional footage.


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It's a well-known fact that the blockbuster combination -Suriya, director KV Anand and music composer Harris Jayaraj are once again coming together for a Tamil film. While the shooting is expected to commence later in June, it looks like Harris Jayaraj has begun work on the project. The latest report is that Harris Jayaraj has left for London to start composing for the yet to titled film. Notably, Harris and KV Anand have delivered chartbuster albums like 'Ayan' and 'Maatraan'.
To be produced by Lyca Productions, the film will reportedly be made on a lavish budget and will be shot across the world. The film is written by Pattukottai Prabhakar and is likely to release next year. The team is currently finalising the cast and crew of the project. Apparently, KV Anand wants to rope in a big heroine for the film.
Meanwhile, Suriya is presently shooting for 'NGK', which is being directed by Selvaraghavan. Produced by Dream Warrior Pictures, it also stars Sai Pallavi and Rakul Preet Singh in lead roles. 'NGK' is all set to release on Diwali this year. According to reports, the shooting will be wrapped before this June.


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Home World Drake issues first statement on Astroworld Festival
Drake issues first statement on Astroworld Festival
Drake on Monday night issued his first public remarks on the "devastating tragedy" at Travis Scott's Astroworld Festival, where he made a surprise appearance before a stampede of concertgoers led to the deaths of eight people.
"I've spent the past few days trying to wrap my mind around this devastating tragedy," Drake wrote in a post to Instagram.
"My heart is broken for the families and friends of those who lost their lives and for anyone who is suffering," he added.
"I will continue to pray for all of them, and will be of service in any way I can."
Drake joined Scott on stage before the show at Houston's NRG Park was shut down after the deadly crush of fans on Friday night.
Eight people were killed and more than 300 injured in what authorities have called a trampling accident during the first night of the two-day festival.
Scott, 30, is facing widespread criticism for the deaths and has been accused of continuing his set, even as unconscious bodies were pulled from the crowd.
A number of lawsuits have already been filed by concertgoers, including one against both Drake and Scott.
Texas attorney Thomas Henry filed a $1 million-plus lawsuit on behalf of Kristian Paredes, 23, from Austin, who he says was left severely injured after Friday night's concert.
Paredes alleges in the lawsuit that the rappers "put profits over their attendees and allowed the deadly show to go on" and "incited the crowd."
Travis Scott SICKO MODE performance at Astrofest 2021 with Drake.
Among those injured in the stampede was a 9-year-old boy who is now clinging to life in coma after suffering injuries to his organs.
"He's a small innocent child — he didn't deserve that, he didn't deserve that at all," the boy's grandfather told a local television station.
Drake and Travis Scott embrace at Astroworld Festival in Houston.
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Aus10™ Rocks: 10 Amazing Local Acts To Get Your Week Started!
By Lauren Gribble
For this week's weekly playlist, we've chosen a variety of Austin bands that will make your week rock! From bands such as Govinda, to John Dee Graham, and Powerburn, we are sure that you will love these 10 Austin acts.
Calvin Russell
Born in Austin, Texas, Calvin Russell joined his first band at 13 called The Caveman. He released his first solo album in 1990 called A Crack in Time. He died in 2011 after battling liver cancer at the age of 62.
Eric Johnson
Eric Johnson began his career in Austin in 1974 when he joined the group The Electromats. He has since been named "one of the most respected guitarists on the planet" by Guitar Player Magazine.
Sara Hickman
Singer-songwriter Sara Hickman moved to Austin in 1995 and has since released over 15 albums in her career. The Texas State Comission of The Arts named Hickman the Official State Musician in 2010.
Ray Campi
Ray Campi moved to Austin in the 1940's with his family, and would go onto become known as "The King of Rockabilly." His trademark is his white double bass, which he sometimes jumps on top of and "rides" while performing.
Arc Attack
ArcAtttack perform their music through a combination of homemade, high-tech, traditional instruments. They auditioned for America's Got Talent in 2010 in the show's fifth season.
With relaxing sounds throughout their music, Govinda is a mellow band that every Austinite should know about. With tracks such as "Decadence" there is no better band to start your week off with then Govinda.
Jimmy Dale Gilmore
With songs such as "I Think I'm Going to Go Downtown," Austin's Jimmy Dale Gilmore writes exceptional country tunes that will remind listeners of Willie Nelson for his real and honest songwriting.
Jon Dee Graham
Landing a spot on the Ladder 49 soundtrack (2004) Jon Dee Graham is a well-known musical figure around Austin. With songs such as "Big Sweet Life," you won't be able to get enough of this local guitarist this week.
Stars of the Lid
Reminding some listeners of Explosions In The Sky, Stars of The Lid are the perfect band to start off your weekend with, allowing you to ease into Monday morning without any problems. Check out the song "A Meaningful Moment Through a Meaning (Less) Process" to see what we mean.
Powderburn
Powerburn, a local metal act, will certainly take your energy levels up a notch this week, as they pound their instruments with meaning and passion. Being loud and forceful is what Powerburn is all about and we can't get enough of their songs.
Featured photo: Eric Johnson, Max Crace
If you would like to read more of Lauren Gribble's features, you can head to her website Listen Here Reviews.
America's Got Talent,
ArcAttack,
Austin music,
Calvin Russell,
Eric Johnson,
Explosions in the Sky,
Govinda,
Guitar Player Magazine,
Jimmy Dale Gilmore,
John Dee Graham,
Powerburn,
Ray Campi,
Sara Hickman,
Starts of the Lid,
The Texas State Commsion of the Arts,
- January 7, 2022
Austin undoubtably loves street art but this week an iconic mural got vandalized. But even the original artist is behind this message.
Wishing you were on a break from cedar fever? We totally know the feeling. That's why we rounded up a few remedies that might help you keep your head clear.
North Burnet
Your guide to living in the Crestview neighborhood including restaurants, coffee shops, parks, and more!


Using the oppression of robots as a metaphor for the oppression of people is an old, old science fiction trope. What better way to demonstrate the evils of treating people as things than to make up a world where there's literally a whole class of people whom everyone believes to be things? That metaphor is, in fact, where the word "robot" comes from — Karol Capek's play R.U.R., which coined the term "robot" from the Czech word "robota," or slave labor.
Since 1939's "I, Robot" by Eando Binder we've seen the trope of the robot as a stand-in for enslaved workers or oppressed ethnic minorities over and over again — more recently with the not-very-subtle class-revolution rhetoric of the Machine Uprisings in works like AI or Battlestar Galactica or the backstory of The Matrix trilogy (which goes so far as to name the first robot rebel, "B1-66-ER," after Bigger Thomas from Richard Wright's Native Son).
And that's great so far as it goes, although there's pretty good arguments against using robots who really are fundamentally different from human beings on every level as a metaphor for fellow human beings who are only different from us because of skin color and history. I've talked about how comparing oppressed people to beings with literal superhuman powers doesn't always teach the lessons we want it to.
And even though I think we're likely to be taken by surprise how much human nature affects the way our technology works — and fails to work — taking this trope as a literal warning about the future seems silly to me. Science fiction movies love to work with the mystical belief that giving machines a human voice and a human shape means that, by sympathetic magic, they will suddenly develop human feelings and human values.
But unless we actually set out to mimic humans as a goal, machines magically turning into people just doesn't happen. It's not how machines work. The fact that the GPS on my iPhone is designed to speak with a human voice and interpret human language doesn't make it any more likely to become a person than the car I'm driving it in.
Which is why I was prepared to be annoyed by the concept of the "Synths" in Channel 4 show Humans, coming to the States on AMC on Sunday, June 28.
Yes, the portrayal of the Synths represents a triumph on the part of the actors — Synths are externally identical to humans in every way, and yet throughout the series we can immediately tell who's a Synth and who isn't because of how the actors hold their faces and bodies (with a little help from makeup and bright green contact lenses). Gemma Chan deserves mad props for her success at the catch-22 of playing the lead Synth as the one "different" robot, Anita — putting just enough of a trace of humanity in her performance to leave you (and her new owners) with lingering doubts.
But what I found unexpectedly compelling about Humans is, well, the humans. The more urgent question than what technological advances are doing to our machines is what those advances are doing to us.
The core plot thread of Humans is the harried Hawkins family finally giving in to modern times and buying a household Synth to take care of the kids while both parents are at work, despite the misgivings of the mom, Laura Hawkins (The IT Crowd's Katherine Parkinson).
Yes, there's a requisite action-packed backstory involving the fact that their new Synth Anita is really one of a tiny band of experimental Synths with the capacity to feel true human emotions, who are therefore being hunted by a shadowy government conspiracy. Yes, that leaves us asking whether Laura's instinctive dislike of Anita is prompted by paranoia over being "replaced" or sensing that Anita is truly different, and what actions Anita might take against Laura if she decides she's a threat — a sci-fi version of The Hand That Rocks the Cradle.
It's this psychodrama/thriller stuff that leaves me cold, mainly because I feel like I've seen it before, although there's enough twists and turns in the first few screener episodes I saw that made me curious as to whether it gets better.
The show asks us not just about the plight of the slave but of the slave master — what does it do to you, to your emotional maturity, to your self-awareness and your self-control, to your soul when you have the power to make someone else do whatever you want?
The fear of computers taking our jobs is the oldest science-fiction scare story — in fact, it pre-dates digital computers and even electricity.
But it's also the fear that makes the most sense, much more sense than the fear of our machines going mad and murdering us or becoming human and falling in love with us. It's happening, all around us, right now.
As is the sense that the more we become obsolete as producers, the more demanding we become as consumers — Mattie openly tells Laura she abuses Synths and treats Anita cruelly and tries to hack into a Synth at school because it's the only power she has.
Humans baldly states its core theme in the form of an interview with a Synth researcher about the ongoing economic crisis caused by the "Synth revolution." The researcher calmly provides the answer we're all used to hearing — that the "fulfillment of work" is overrated, that most of the people working in most of the world today find work to be a backbreaking nightmare.
Humans throws that assumption right in our face. We, as middle-class citizens of the UK and the US watching this show, by this argument are "freer" than anyone else in history has been — free to consume as much entertainment and information and goods and services as the Web can deliver. Does this make us better than our ancestors? Happier? More "human"?
This isn't revolutionary. Where Humans might be revolutionary is asking if that might not be a good thing. Not for the machines, for us — to free us from the chains on our souls that come with being slave masters.


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You are here: Home News Crime UPDATE: Chicago's Bloody Christmas Weekend Thankfully Ends; 2016 Expected to Be Third Highest
UPDATE: Chicago's Bloody Christmas Weekend Thankfully Ends; 2016 Expected to Be Third Highest
Category: Crime
Chicago's bloody rampage continued Monday with a sharp spike in shootings and with five days before New Year's Eve the 61 shootings, 50 wounded and 11 homicides, over the three-day holiday weekend bring the 2016 total to 785 homicides.
The alarming murder rate, which has increased more than 50% over the 476 total of 2015, increases in shocking numbers weekly.
December killings and wounded to date bring the totals to 45 shot and killed, 189 shot and wounded with 234 total shootings and 48 total homicides.
From December 18 through December 24 the total shot and killed ceased at one per day or 7 for the week; Shot and Wounded, 57 for a total of 64 victims of gun violence and 8 total homicides.
2016 is shaping up to be the third worst murder rate in Chicago's history with a total of 705 shot and killed, dead at the scene from gun related violence. A shocking 3612 victims were shot and wounded with a total of 4317 suffering from gun violence. The total homicides, for 2016 with six days before the year ends and forecasting a bloody violent New Year's Eve, is 785 murdered.
The possibility of an extremely cold weather pattern may slow some of the violence over the next six days.
Battleground Chi-raq: Taming Chicago's Rising Murder Rate
However, it appears Chi-raq, with a person shot every 2:00 minutes and a person murdered every 11:00 minutes, with 708 males killed and 3,197 wounded leaving 63 females murdered and 366 wounded.
Statistics show the majority of homicides, a whopping 78.2% of all gun violence is black on black crime. Gang violence is the primary cause of the extremely high interracial murder rate. Exponentially Decreasing exponentially would be Hispanic population responsible for 16.8 of the race on race violence and decreasing further white or Caucasians are responsible for less than 5% of all white on white gun violence.
Drive by shootings may be a built-in component of Chicago's gang violence and statically the mass murder four or more victims at a single scene only amounts to 34 shootings and 17 murders. The Hat Trick, a slang term for three victims shot at a single scene, accounted for 93 of the shootings and 33 deaths. Attempts at double homicides seem to the choice of most gun violence with a stunning 437 shootings resulting in 137 killed.
Chicago, like any major city, has areas of heavier crime and neighborhoods in cities can be simply crossing a main street and the neighborhood can change from Chinatown to Little Italy as in New York City.
CHI-RAQ Review - Spike Lee's Timely Gangland Gun Violence Pic Hits a Bulls Eye
For resident of Chicago, gun violence and homicides are highest in Austin, with 89 murders and 443 wounded totaling 532 victims, Englewood has 85 homicides and 349 wounded, totaling 434 victims; Garfield Park is third with 57 homicides and 324 wounded totaling 381 victims.
New City, North Lawndale and Grand Crossing are the next three homicide heavy neighborhoods with 108 murders total. Fifteen neighborhoods in Chicago area are known for homicides, the remainder of gun related crime happens outside these 15 neighborhoods and totals 249 of the 748 homicides to date.
More than 80% of all gun related crimes in Chicago remain unsolved.
Chicago's homicide rate which stuns the world is not the highest and unless there is an exceptionally bloody six days, an all-out war, the numbers even if they increase to 800 will still rank third overall with 970 in 1974 as the highest, 943 in 1992 coming in second and 2016 third.
Image coutesy of Google search; Statistics courtesy of www.heyjackass.com
Celebrity Interview: Talking With Teyonah Parris, CHI-RAQ Star, on Spike Lee, Gun Violence and Angela Bassett
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Defamation Review: Powerful, Dramatic and Poignant from Director Yoav Shamir
"Defamation," a documentary that explores Director Yoav Shamir's personal views of Anti-Semitism, the Holocaust and Nazi's, in a world where the only opinions are the traditional hardline views and begs the question of its value in a post-Hitler world.
Notre-Dame Tentée Par Le Privé ?
L'incendie de Notre-Dame de Paris pose en filigrane la question du financement des travaux d'entretien des édifices religieux placés sous le contrôle d'un Etat endetté et tenté par l'appel au privé pour sauver un patrimoine au temps compté.
Robb Vices Luxury Subscription - The Haute Life Delivered
Robb Report, a name synonymous with luxury lifestyles the world over, has initiated a new membership subscription service which allows those who pursue of the good life to have delicious, luxurious haute items delivered monthly.
Beltway Insider: Obama Responds as Ebola Hits US; Global Coalition Grows; September Job Numbers
President Obama and Vice President Joseph Biden have continued to galvanize a global coalition determined to dismantle and destroy ISIS/ISIL even as it continues to grow and taunt both the United States and the United Kingdom with execution of hostages.
Celebrity Real State News: Enrique's Former Miami Mansion, with Prime Bay and Skyline Views, On Market
The Iglesias men cover a wide range of music genres. Father Julio, now 73, with his chiseled features, deeply romantic songs, and smooth bedroom voice, with a law degree on the side, has sold over 120 million records.
Beltway Insider: Obama/Trickledown Agenda; Students/Journos Murdered; Flint; Killer Winter Storm
President Barack Obama met this week, for last time as he embarks on his end of term duties, with America's Mayors hoping to motivate them to see beyond the chronic challenges that may not present solutions under their term.
Cold Grey Light of Dawn, Newest Single by Hudson Moore, Featured in Sweetwater
"Cold Grey Light of Dawn," Hudson Moore's newest song is featured in the end credits of the recently released revenge filled western, "Sweetwater," which stars January Jones, Ed Harris and Jason Isaacs.
HL Tech: A Guide Through The VR Craze And The 25 Headsets On The Market Now
Smartphone dependence is a major variable separating different classes of virtual reality headsets. Some fun, functional VR units can be purchased for under $50, but require outside hardware for processing and audio. Other units cost more, but are completely — or mostly — self-contained.
Money News: Global Markets Tumble; Sensex Survives
The Dow Jones Industrial, fighting the Bear market, managed to rally steadily throughout the week, with only minor setbacks the DOW wasn't able to pull itself out of the firmly held grasp of the bear market and closed down.
Shangri-La Barr Al Jissah Resort & Spa, Sultanate of Oman Receives Silver Medal at The Dilmah Real High Tea Global Challenge 2015
Shangri-La Barr Al Jissah Resort & Spa, Sultanate of Oman have received a silver medal at the final of the Dilmah Real High Tea Global Challenge 2015 held at the Hilton Residency, Sri Lanka.
Beltway Insider: Trump Nat'l Emergency, Israeli PM Election, Venezuela Erupts, El Chapo Jury, Kraft Shocker, ISIS Brides, Bernie Sanders
President Trump has doubled down on his efforts to secure funding for the Border Wall, which he believes will perform multi-purposes in the fight against illegal immigration by stopping the entry of illegals crime will also fall.
Manscaped Launches The Second-Generation Trimmer for Down Under Male Grooming
Manscaped, Inc., the world's #1 brand for below-the-waist male grooming, has started shipping, The Lawn Mower 2.0™ – an ergonomically-designed trimmer that redefines power, precision, and sensitivity, with snap-in blade replacement, it takes men's health and hygiene to a new level!
Donnie Wahlberg Rocks Chicagoland Raising $759k to Help Kids with Autism for Generation Rescue (Photos)
New Kids On The Block member Donnie Wahlberg joined forces with Generation Rescue for Another Evening with Donnie Wahlberg and Special Guests concert, raising $759,000 to spread awareness and help fund autism treatment for low-income and at-risk families.
Beltway Insider: Obama Welcomes French Pres to WH; Climate Summit; PP Shooting; Medal Honorees
President Obama bestowed the Presidential Medal of Freedom, the highest civilian honor, upon sixteen leaders, ranging from Hollywood icons to legal scholars to sports legends, for acts of bravery, of brilliance, of unwavering dedication to the strength of the nation.
Money News: World Markets Rebound; DOW Up, American Markets Steady
The US Markets continued to show strong signs of steady growth, with Asian and European Markets also showing signs of consumer confidence, as shoppers are positively responding to consumer friendly incentives and the November Jobs report caps a year of economic growth to end 2014.


Vacation Advice – Planning For An Affordable Beach Vacation!
There are plenty of places you can drive to in the USA affordably. You can either rent a car or go in your own vehicle. There are some limitations of renting a car. For example, some rental services do not allow their cars to go out of a particular state. For those who are not too familiar with the roads, this can be a bit of trouble. Make sure you are aware of all of them.
In the good old days, if you wanted to buy something you found out how much it would cost, you saved up the money, and you bought whatever it was that you wanted. Not in today's "instant gratification" culture. Now you don't need the money to buy whatever you want, you just need a little plastic card – and apparently most families have five of them to choose from!
The III reported dismal statistics in 2007 on apprehending car thieves, with an arrest rate of only 12.6 percent. Furthermore, the the National Insurance Crime Bureau reported that year that 41 percent of stolen vehicles were never recovered. If your car is stolen, there isn't much you can do after the fact except call the police and file an insurance claim. Meanwhile, you won't have transportation unless you either car and driver hire sri lanka or go out and buy another one. It's much better to take the following precautions to prevent car theft before it happens to you.
Credit card companies know that when students can not pay their balances, they have the parents save them. They also offer attractive interest rates and benefits to college students because college is the time when most people get their first credit cards. Most people stick to their first credit card even after graduation. So, college students are great customers!
Save on Petrol. If you do not need a SUV or MPV, simply book a simple sedan. The cost of petrol in Singapore isn't cheap and it is definitely smarter to use something you need.
Seeing the Grand Canyon by air is the ultimate way to see this national treasure. Be it West Rim or South Rim, you'll see pretty much see it all. These airplane tours can be expanded to include helicopter flights, rafting trips, and Skywalk passes, and Las Vegas flyovers. They are also the fastest way to go from Las Vegas to the South Rim. These trips are economical, too, especially if you book them online, where you can get up to 35% off. So kick off your shoes, recline your seat, and prepare for departure. Getting to the Grand Canyon and seeing it in all its natural glory has never been easier.