diff --git a/app-proto/src/diagnostics.rs b/app-proto/src/diagnostics.rs
index d283c51..0aa46c3 100644
--- a/app-proto/src/diagnostics.rs
+++ b/app-proto/src/diagnostics.rs
@@ -2,7 +2,7 @@ use charming::{
     Chart,
     WasmRenderer,
     component::{Axis, DataZoom, Grid},
-    element::AxisType,
+    element::{AxisType, Symbol},
     series::{Line, Scatter},
 };
 use sycamore::prelude::*;
@@ -50,6 +50,10 @@ fn RealizationStatus() -> View {
     }
 }
 
+fn into_time_point((step, value): (usize, f64)) -> Vec<Option<f64>> {
+    vec![Some(step as f64), Some(value)]
+}
+
 // the loss history from the last realization
 #[component]
 fn LossHistory() -> View {
@@ -60,38 +64,35 @@ fn LossHistory() -> View {
     on_mount(move || {
         create_effect(move || {
             // get the loss history
-            let scaled_loss = state.assembly.descent_history.with(
-                |history| history.scaled_loss.clone()
+            let scaled_loss: Vec<_> = state.assembly.descent_history.with(
+                |history| history.scaled_loss
+                    .iter()
+                    .enumerate()
+                    .map(|(step, &loss)| (step, loss))
+                    .map(into_time_point)
+                    .collect()
             );
-            let step_cnt = scaled_loss.len();
             
             // initialize the chart axes and series
-            const MIN_INTERVAL: f64 = 0.01;
-            let mut step_axis = Axis::new()
+            let step_axis = Axis::new()
                 .type_(AxisType::Category)
                 .boundary_gap(false);
-            let scaled_loss_axis = Axis::new()
-                .type_(AxisType::Value)
-                .min(0)
-                .min_interval(MIN_INTERVAL);
+            let scaled_loss_axis = Axis::new().type_(AxisType::Log);
             
             // load the chart data. when there's no history, we load the data
             // point (0, None) to clear the chart. it would feel more natural to
             // load empty data vectors, but that turns out not to clear the
             // chart: it instead leads to previous data being re-used
-            let mut scaled_loss_series = Line::new();
-            if step_cnt > 0 {
-                step_axis = step_axis.data(
-                    (0..step_cnt).map(|step| step.to_string()).collect()
-                );
-                scaled_loss_series = scaled_loss_series.data(scaled_loss);
-            } else {
-                step_axis = step_axis.data(vec![0.to_string()]);
-                scaled_loss_series = scaled_loss_series.data(vec![None::<f64>]);
-            }
+            let scaled_loss_series = Line::new().data(
+                if scaled_loss.len() > 0 {
+                    scaled_loss
+                } else {
+                    vec![vec![Some(0.0), None::<f64>]]
+                }
+            );
             let chart = Chart::new()
                 .animation(false)
-                .data_zoom(DataZoom::new().y_axis_index(0).right(40).start(0).end(100))
+                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
                 .x_axis(step_axis)
                 .y_axis(scaled_loss_axis)
                 .grid(Grid::new().top(20).right(80).bottom(30).left(60))
@@ -114,41 +115,73 @@ fn SpectrumHistory() -> View {
     
     on_mount(move || {
         create_effect(move || {
-            // get the spectrum of the Hessian at each step
-            let hess_eigvals = state.assembly.descent_history.with(
+            // get the spectrum of the Hessian at each step, split into its
+            // positive and negative parts. throw away eigenvalues that are
+            // close to zero
+            const ZERO_THRESHOLD: f64 = 1e-6;
+            let (
+                hess_eigvals_pos,
+                hess_eigvals_neg
+            ): (Vec<_>, Vec<_>) = state.assembly.descent_history.with(
                 |history| history.hess_eigvals
                     .iter()
                     .enumerate()
                     .map(
-                        |(step, eigvals)| eigvals.iter().map(
-                            move |val| vec![step as f64, *val]
-                        )
+                        |(step, eigvals)| eigvals
+                            .iter()
+                            .filter(|&&val| val.abs() > ZERO_THRESHOLD)
+                            .map(
+                                move |&val| (step, val)
+                            )
                     )
                     .flatten()
-                    .collect::<Vec<_>>()
+                    .partition(|&(_, val)| val > 0.0)
             );
             
             // initialize the chart axes and series
-            let step_axis = Axis::new();
-            let eigval_axis = Axis::new();
+            let step_axis = Axis::new()
+                .type_(AxisType::Category)
+                .boundary_gap(false);
+            let eigval_axis = Axis::new().type_(AxisType::Log);
             
             // load the chart data. when there's no history, we load the data
             // point (0, None) to clear the chart. it would feel more natural to
             // load empty data vectors, but that turns out not to clear the
             // chart: it instead leads to previous data being re-used
-            let mut eigval_series = Scatter::new().symbol_size(7);
-            if hess_eigvals.len() > 0 {
-                eigval_series = eigval_series.data(hess_eigvals);
-            } else {
-                eigval_series = eigval_series.data(vec![None::<f64>, None::<f64>]);
-            }
+            let eigval_series_pos = Scatter::new()
+                .symbol_size(4.5)
+                .data(
+                    if hess_eigvals_pos.len() > 0 {
+                        hess_eigvals_pos
+                            .into_iter()
+                            .map(into_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
+            let eigval_series_neg = Scatter::new()
+                .symbol(Symbol::Diamond)
+                .symbol_size(6.0)
+                .data(
+                    if hess_eigvals_neg.len() > 0 {
+                        hess_eigvals_neg
+                            .into_iter()
+                            .map(|(step, val)| (step, -val))
+                            .map(into_time_point)
+                            .collect()
+                    } else {
+                        vec![vec![Some(0.0), None::<f64>]]
+                    }
+                );
             let chart = Chart::new()
                 .animation(false)
-                .data_zoom(DataZoom::new().y_axis_index(0).right(40).start(0).end(100))
+                .data_zoom(DataZoom::new().y_axis_index(0).right(40))
                 .x_axis(step_axis)
                 .y_axis(eigval_axis)
                 .grid(Grid::new().top(20).right(80).bottom(30).left(60))
-                .series(eigval_series);
+                .series(eigval_series_pos)
+                .series(eigval_series_neg);
             renderer.render(CONTAINER_ID, &chart).unwrap();
         });
     });